Proofgold Address

Param atleastp^atleastp : ι → ι → ο
Param u1 : ι
Param Sing^Sing : ι → ι
Known atleastp_tra^atleastp_tra : ∀ x0 x1 x2 . atleastp x0 x1 ⟶ atleastp x1 x2 ⟶ atleastp x0 x2
Param equip^equip : ι → ι → ο
Known equip_atleastp^{equip_atleastp} : ∀ x0 x1 . equip x0 x1 ⟶ atleastp x0 x1
Known equip_sym^equip_sym : ∀ x0 x1 . equip x0 x1 ⟶ equip x1 x0
Known 5169f..^equip_Sing_1 : ∀ x0 . equip (Sing x0) u1
Definition Subq^Subq := λ x0 x1 . ∀ x2 . x2 ∈ x0 ⟶ x2 ∈ x1
Known Subq_atleastp^{Subq_atleastp} : ∀ x0 x1 . x0 ⊆ x1 ⟶ atleastp x0 x1
Known SingE^SingE : ∀ x0 x1 . x1 ∈ Sing x0 ⟶ x1 = x0
Theorem 04353.. : ∀ x0 x1 . x1 ∈ x0 ⟶ atleastp u1 x0 (proof)
Param ordsucc^ordsucc : ι → ι
Definition u2 := ordsucc u1
Param setminus^setminus : ι → ι → ι
Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Definition nIn^nIn := λ x0 x1 . not (x0 ∈ x1)
Param binunion^binunion : ι → ι → ι
Known eb0c4..^{binunion_remove1_eq} : ∀ x0 x1 . x1 ∈ x0 ⟶ x0 = binunion (setminus x0 (Sing x1)) (Sing x1)
Known 1dc5a.. : ∀ x0 x1 x2 . nIn x2 x1 ⟶ atleastp x0 x1 ⟶ atleastp (ordsucc x0) (binunion x1 (Sing x2))
Known setminus_nIn_I2^{setminus_nIn_I2} : ∀ x0 x1 x2 . x2 ∈ x1 ⟶ nIn x2 (setminus x0 x1)
Known SingI^SingI : ∀ x0 . x0 ∈ Sing x0
Known setminusI^setminusI : ∀ x0 x1 x2 . x2 ∈ x0 ⟶ nIn x2 x1 ⟶ x2 ∈ setminus x0 x1
Theorem ada03.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ atleastp u2 x0 (proof)
Definition u3 := ordsucc u2
Theorem 5d098.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x4 : ο . x4) ⟶ (x1 = x3 ⟶ ∀ x4 : ο . x4) ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ atleastp u3 x0 (proof)
Definition u4 := ordsucc u3
Theorem 09d70.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x5 : ο . x5) ⟶ (x1 = x3 ⟶ ∀ x5 : ο . x5) ⟶ (x2 = x3 ⟶ ∀ x5 : ο . x5) ⟶ (x1 = x4 ⟶ ∀ x5 : ο . x5) ⟶ (x2 = x4 ⟶ ∀ x5 : ο . x5) ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ atleastp u4 x0 (proof)
Definition u5 := ordsucc u4
Theorem 368c2.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x3 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x5 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x5 ⟶ ∀ x6 : ο . x6) ⟶ (x3 = x5 ⟶ ∀ x6 : ο . x6) ⟶ (x4 = x5 ⟶ ∀ x6 : ο . x6) ⟶ atleastp u5 x0 (proof)
Definition u6 := ordsucc u5
Theorem 2e3d8.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x3 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x3 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x4 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x4 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x4 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x1 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x6 ⟶ ∀ x7 : ο . x7) ⟶ (x5 = x6 ⟶ ∀ x7 : ο . x7) ⟶ atleastp u6 x0 (proof)
Definition u7 := ordsucc u6
Theorem 19e0f.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x8 : ο . x8) ⟶ (x1 = x3 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x3 ⟶ ∀ x8 : ο . x8) ⟶ (x1 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x4 ⟶ ∀ x8 : ο . x8) ⟶ (x1 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x5 ⟶ ∀ x8 : ο . x8) ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x1 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x7 ⟶ ∀ x8 : ο . x8) ⟶ (x6 = x7 ⟶ ∀ x8 : ο . x8) ⟶ atleastp u7 x0 (proof)
Definition u8 := ordsucc u7
Theorem 75f77.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x3 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x3 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x4 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x4 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x4 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x5 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x1 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x8 ⟶ ∀ x9 : ο . x9) ⟶ (x7 = x8 ⟶ ∀ x9 : ο . x9) ⟶ atleastp u8 x0 (proof)
Definition u9 := ordsucc u8
Theorem 04f57.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x3 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x3 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x4 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x4 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x4 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x6 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x1 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x9 ⟶ ∀ x10 : ο . x10) ⟶ (x8 = x9 ⟶ ∀ x10 : ο . x10) ⟶ atleastp u9 x0 (proof)
Definition u10 := ordsucc u9
Theorem d140d.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x3 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x3 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x4 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x4 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x4 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x5 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x5 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x5 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x5 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x6 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x6 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x6 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x6 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x6 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x8 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x1 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x10 ⟶ ∀ x11 : ο . x11) ⟶ (x9 = x10 ⟶ ∀ x11 : ο . x11) ⟶ atleastp u10 x0 (proof)
Definition u11 := ordsucc u10
Theorem 09f2a.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x3 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x3 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x4 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x4 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x4 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x5 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x5 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x5 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x5 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x6 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x6 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x6 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x6 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x6 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x7 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x7 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x7 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x7 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x7 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x7 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x8 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x9 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x1 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x11 ⟶ ∀ x12 : ο . x12) ⟶ (x10 = x11 ⟶ ∀ x12 : ο . x12) ⟶ atleastp u11 x0 (proof)
Definition u12 := ordsucc u11
Theorem 8d9d9.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x3 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x3 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x5 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x5 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x5 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x5 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x6 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x6 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x6 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x6 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x6 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x7 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x7 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x7 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x7 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x7 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x7 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x8 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x9 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x10 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x1 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x12 ⟶ ∀ x13 : ο . x13) ⟶ (x11 = x12 ⟶ ∀ x13 : ο . x13) ⟶ atleastp u12 x0 (proof)
Definition u13 := ordsucc u12
Theorem 6fc5a.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x3 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x3 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x4 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x4 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x4 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x5 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x5 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x5 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x5 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x6 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x6 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x6 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x6 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x6 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x7 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x7 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x7 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x7 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x7 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x7 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x8 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x9 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x10 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x10 = x11 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x10 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x11 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x1 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x10 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x11 = x13 ⟶ ∀ x14 : ο . x14) ⟶ (x12 = x13 ⟶ ∀ x14 : ο . x14) ⟶ atleastp u13 x0 (proof)
Definition u14 := ordsucc u13
Theorem 1565e.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x3 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x3 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x4 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x4 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x4 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x5 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x5 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x5 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x5 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x6 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x6 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x6 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x6 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x6 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x7 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x7 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x7 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x7 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x7 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x7 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x8 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x8 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x9 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x8 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x9 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x10 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x8 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x9 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x10 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x11 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x8 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x9 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x10 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x11 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x12 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x1 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x8 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x9 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x10 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x11 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x12 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x13 = x14 ⟶ ∀ x15 : ο . x15) ⟶ atleastp u14 x0 (proof)
Definition u15 := ordsucc u14
Theorem 1fbf0.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x3 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x3 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x4 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x4 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x4 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x5 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x5 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x5 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x5 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x6 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x6 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x6 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x6 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x6 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x7 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x7 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x7 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x7 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x7 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x7 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x8 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x9 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x9 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x10 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x9 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x10 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x11 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x9 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x10 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x11 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x12 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x9 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x10 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x11 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x12 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x13 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x1 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x2 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x9 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x10 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x11 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x12 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x13 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x14 = x15 ⟶ ∀ x16 : ο . x16) ⟶ atleastp u15 x0 (proof)
Definition u16 := ordsucc u15
Theorem 24b48.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x3 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x3 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x4 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x4 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x4 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x5 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x5 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x5 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x5 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x6 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x6 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x6 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x6 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x6 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x7 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x7 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x7 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x7 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x7 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x7 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x8 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x9 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x10 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x10 = x11 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x10 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x11 = x12 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x10 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x11 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x12 = x13 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x10 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x11 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x12 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x13 = x14 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x10 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x11 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x12 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x13 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x14 = x15 ⟶ ∀ x17 : ο . x17) ⟶ (x1 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x2 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x3 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x4 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x5 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x6 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x7 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x8 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x9 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x10 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x11 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x12 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x13 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x14 = x16 ⟶ ∀ x17 : ο . x17) ⟶ (x15 = x16 ⟶ ∀ x17 : ο . x17) ⟶ atleastp u16 x0 (proof)
Definition u17 := ordsucc u16
Theorem 9efa7.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x3 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x3 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x4 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x4 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x4 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x5 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x5 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x5 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x5 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x6 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x6 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x6 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x6 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x6 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x7 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x7 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x7 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x7 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x7 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x7 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x8 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x9 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x10 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x11 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x11 = x12 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x11 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x12 = x13 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x11 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x12 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x13 = x14 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x11 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x12 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x13 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x14 = x15 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x11 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x12 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x13 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x14 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x15 = x16 ⟶ ∀ x18 : ο . x18) ⟶ (x1 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x2 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x3 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x4 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x5 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x6 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x7 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x8 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x9 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x10 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x11 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x12 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x13 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x14 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x15 = x17 ⟶ ∀ x18 : ο . x18) ⟶ (x16 = x17 ⟶ ∀ x18 : ο . x18) ⟶ atleastp u17 x0 (proof)
Definition u18 := ordsucc u17
Theorem 74326.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x3 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x3 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x4 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x4 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x4 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x5 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x5 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x5 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x5 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x6 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x6 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x6 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x6 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x6 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x7 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x7 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x7 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x7 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x7 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x7 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x8 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x9 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x10 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x11 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x12 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x12 = x13 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x12 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x13 = x14 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x12 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x13 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x14 = x15 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x12 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x13 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x14 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x15 = x16 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x12 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x13 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x14 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x15 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x16 = x17 ⟶ ∀ x19 : ο . x19) ⟶ (x1 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x2 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x3 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x4 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x5 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x6 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x7 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x8 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x9 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x10 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x11 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x12 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x13 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x14 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x15 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x16 = x18 ⟶ ∀ x19 : ο . x19) ⟶ (x17 = x18 ⟶ ∀ x19 : ο . x19) ⟶ atleastp u18 x0 (proof)
Definition u19 := ordsucc u18
Theorem 8ca1e.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x3 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x3 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x4 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x4 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x4 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x5 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x5 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x5 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x5 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x6 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x6 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x6 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x6 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x6 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x7 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x7 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x7 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x7 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x7 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x7 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x8 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x9 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x10 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x11 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x12 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x13 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x13 = x14 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x13 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x14 = x15 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x13 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x14 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x15 = x16 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x13 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x14 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x15 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x16 = x17 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x13 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x14 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x15 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x16 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x17 = x18 ⟶ ∀ x20 : ο . x20) ⟶ (x1 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x2 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x3 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x4 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x5 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x6 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x7 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x8 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x9 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x10 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x11 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x12 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x13 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x14 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x15 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x16 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x17 = x19 ⟶ ∀ x20 : ο . x20) ⟶ (x18 = x19 ⟶ ∀ x20 : ο . x20) ⟶ atleastp u19 x0 (proof)
Definition u20 := ordsucc u19
Theorem f67f7.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x3 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x3 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x4 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x4 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x4 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x5 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x5 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x5 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x5 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x6 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x6 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x6 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x6 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x6 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x7 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x7 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x7 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x7 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x7 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x7 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x8 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x9 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x10 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x11 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x12 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x13 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x14 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x14 = x15 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x14 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x15 = x16 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x14 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x15 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x16 = x17 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x14 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x15 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x16 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x17 = x18 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x14 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x15 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x16 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x17 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x18 = x19 ⟶ ∀ x21 : ο . x21) ⟶ (x1 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x2 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x3 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x4 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x5 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x6 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x7 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x8 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x9 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x10 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x11 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x12 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x13 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x14 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x15 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x16 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x17 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x18 = x20 ⟶ ∀ x21 : ο . x21) ⟶ (x19 = x20 ⟶ ∀ x21 : ο . x21) ⟶ atleastp u20 x0 (proof)
Definition u21 := ordsucc u20
Theorem 084ef.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x3 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x3 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x4 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x4 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x4 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x5 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x5 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x5 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x5 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x6 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x6 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x6 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x6 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x6 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x7 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x7 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x7 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x7 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x7 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x7 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x8 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x9 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x10 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x11 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x12 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x13 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x14 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x15 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x15 = x16 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x15 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x16 = x17 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x15 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x16 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x17 = x18 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x15 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x16 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x17 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x18 = x19 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x15 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x16 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x17 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x18 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x19 = x20 ⟶ ∀ x22 : ο . x22) ⟶ (x1 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x2 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x3 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x4 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x5 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x6 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x7 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x8 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x9 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x10 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x11 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x12 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x13 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x14 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x15 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x16 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x17 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x18 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x19 = x21 ⟶ ∀ x22 : ο . x22) ⟶ (x20 = x21 ⟶ ∀ x22 : ο . x22) ⟶ atleastp u21 x0 (proof)
Definition u22 := ordsucc u21
Theorem 984c8.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x3 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x3 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x4 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x4 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x4 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x5 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x5 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x5 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x5 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x6 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x6 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x6 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x6 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x6 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x7 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x7 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x7 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x7 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x7 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x7 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x8 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x9 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x10 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x11 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x12 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x13 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x14 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x15 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x16 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x16 = x17 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x16 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x17 = x18 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x16 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x17 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x18 = x19 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x16 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x17 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x18 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x19 = x20 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x16 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x17 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x18 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x19 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x20 = x21 ⟶ ∀ x23 : ο . x23) ⟶ (x1 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x2 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x3 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x4 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x5 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x6 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x7 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x8 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x9 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x10 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x11 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x12 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x13 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x14 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x15 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x16 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x17 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x18 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x19 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x20 = x22 ⟶ ∀ x23 : ο . x23) ⟶ (x21 = x22 ⟶ ∀ x23 : ο . x23) ⟶ atleastp u22 x0 (proof)
Definition u23 := ordsucc u22
Theorem e6da2.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x3 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x3 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x4 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x4 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x4 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x5 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x5 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x5 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x5 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x6 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x6 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x6 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x6 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x6 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x7 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x7 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x7 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x7 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x7 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x7 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x8 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x9 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x10 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x11 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x12 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x13 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x14 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x15 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x16 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x17 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x17 = x18 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x17 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x18 = x19 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x17 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x18 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x19 = x20 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x17 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x18 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x19 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x20 = x21 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x17 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x18 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x19 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x20 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x21 = x22 ⟶ ∀ x24 : ο . x24) ⟶ (x1 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x2 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x3 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x4 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x5 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x6 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x7 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x8 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x9 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x10 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x11 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x12 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x13 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x14 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x15 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x16 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x17 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x18 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x19 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x20 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x21 = x23 ⟶ ∀ x24 : ο . x24) ⟶ (x22 = x23 ⟶ ∀ x24 : ο . x24) ⟶ atleastp u23 x0 (proof)
Definition u24 := ordsucc u23
Theorem cd18c.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x3 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x3 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x4 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x4 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x4 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x5 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x5 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x5 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x5 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x6 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x6 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x6 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x6 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x6 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x7 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x7 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x7 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x7 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x7 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x7 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x8 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x9 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x10 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x11 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x12 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x13 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x14 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x15 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x16 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x17 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x18 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x18 = x19 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x18 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x19 = x20 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x18 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x19 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x20 = x21 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x18 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x19 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x20 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x21 = x22 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x18 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x19 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x20 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x21 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x22 = x23 ⟶ ∀ x25 : ο . x25) ⟶ (x1 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x2 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x3 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x4 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x5 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x6 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x7 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x8 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x9 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x10 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x11 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x12 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x13 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x14 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x15 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x16 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x17 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x18 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x19 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x20 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x21 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x22 = x24 ⟶ ∀ x25 : ο . x25) ⟶ (x23 = x24 ⟶ ∀ x25 : ο . x25) ⟶ atleastp u24 x0 (proof)
Definition u25 := ordsucc u24
Theorem 7ee90.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x3 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x3 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x4 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x4 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x4 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x5 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x5 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x5 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x5 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x6 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x6 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x6 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x6 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x6 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x7 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x7 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x7 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x7 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x7 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x7 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x8 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x9 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x10 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x11 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x12 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x13 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x14 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x15 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x16 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x17 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x18 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x19 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x19 = x20 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x19 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x20 = x21 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x19 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x20 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x21 = x22 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x19 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x20 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x21 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x22 = x23 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x19 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x20 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x21 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x22 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x23 = x24 ⟶ ∀ x26 : ο . x26) ⟶ (x1 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x2 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x3 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x4 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x5 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x6 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x7 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x8 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x9 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x10 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x11 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x12 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x13 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x14 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x15 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x16 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x17 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x18 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x19 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x20 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x21 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x22 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x23 = x25 ⟶ ∀ x26 : ο . x26) ⟶ (x24 = x25 ⟶ ∀ x26 : ο . x26) ⟶ atleastp u25 x0 (proof)
Definition u26 := ordsucc u25
Theorem 79bd2.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x3 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x3 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x4 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x4 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x4 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x5 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x5 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x5 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x5 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x6 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x6 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x6 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x6 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x6 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x7 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x7 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x7 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x7 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x7 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x7 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x8 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x9 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x10 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x11 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x12 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x13 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x14 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x15 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x16 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x17 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x18 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x19 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x20 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x20 = x21 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x20 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x21 = x22 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x20 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x21 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x22 = x23 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x20 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x21 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x22 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x23 = x24 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x20 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x21 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x22 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x23 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x24 = x25 ⟶ ∀ x27 : ο . x27) ⟶ (x1 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x2 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x3 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x4 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x5 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x6 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x7 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x8 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x9 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x10 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x11 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x12 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x13 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x14 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x15 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x16 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x17 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x18 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x19 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x20 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x21 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x22 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x23 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x24 = x26 ⟶ ∀ x27 : ο . x27) ⟶ (x25 = x26 ⟶ ∀ x27 : ο . x27) ⟶ atleastp u26 x0 (proof)
Definition u27 := ordsucc u26
Theorem b36ff.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x3 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x3 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x4 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x4 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x4 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x5 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x5 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x5 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x5 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x6 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x6 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x6 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x6 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x6 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x7 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x7 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x7 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x7 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x7 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x7 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x8 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x9 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x10 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x11 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x12 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x13 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x14 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x15 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x16 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x17 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x18 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x19 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x20 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x21 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x21 = x22 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x21 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x22 = x23 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x21 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x22 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x23 = x24 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x21 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x22 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x23 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x24 = x25 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x21 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x22 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x23 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x24 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x25 = x26 ⟶ ∀ x28 : ο . x28) ⟶ (x1 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x2 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x3 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x4 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x5 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x6 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x7 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x8 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x9 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x10 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x11 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x12 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x13 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x14 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x15 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x16 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x17 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x18 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x19 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x20 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x21 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x22 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x23 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x24 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x25 = x27 ⟶ ∀ x28 : ο . x28) ⟶ (x26 = x27 ⟶ ∀ x28 : ο . x28) ⟶ atleastp u27 x0 (proof)
Definition u28 := ordsucc u27
Theorem bf9c0.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x3 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x3 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x4 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x4 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x4 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x5 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x5 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x5 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x5 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x6 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x6 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x6 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x6 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x6 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x7 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x7 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x7 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x7 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x7 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x7 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x8 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x9 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x10 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x11 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x12 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x13 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x14 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x15 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x16 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x17 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x18 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x19 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x20 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x21 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x22 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x22 = x23 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x22 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x23 = x24 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x22 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x23 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x24 = x25 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x22 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x23 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x24 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x25 = x26 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x22 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x23 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x24 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x25 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x26 = x27 ⟶ ∀ x29 : ο . x29) ⟶ (x1 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x2 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x3 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x4 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x5 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x6 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x7 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x8 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x9 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x10 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x11 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x12 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x13 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x14 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x15 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x16 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x17 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x18 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x19 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x20 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x21 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x22 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x23 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x24 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x25 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x26 = x28 ⟶ ∀ x29 : ο . x29) ⟶ (x27 = x28 ⟶ ∀ x29 : ο . x29) ⟶ atleastp u28 x0 (proof)
Definition u29 := ordsucc u28
Theorem 1758f.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ ∀ x29 . x29 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x3 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x3 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x4 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x4 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x4 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x5 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x5 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x5 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x5 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x6 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x6 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x6 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x6 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x6 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x7 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x7 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x7 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x7 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x7 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x7 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x8 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x9 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x10 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x11 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x12 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x13 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x14 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x15 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x16 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x17 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x18 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x19 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x20 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x21 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x22 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x23 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x23 = x24 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x23 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x24 = x25 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x23 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x24 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x25 = x26 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x23 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x24 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x25 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x26 = x27 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x23 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x24 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x25 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x26 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x27 = x28 ⟶ ∀ x30 : ο . x30) ⟶ (x1 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x2 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x3 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x4 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x5 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x6 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x7 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x8 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x9 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x10 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x11 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x12 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x13 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x14 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x15 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x16 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x17 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x18 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x19 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x20 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x21 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x22 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x23 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x24 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x25 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x26 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x27 = x29 ⟶ ∀ x30 : ο . x30) ⟶ (x28 = x29 ⟶ ∀ x30 : ο . x30) ⟶ atleastp u29 x0 (proof)
Definition u30 := ordsucc u29
Theorem ec6bb.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ ∀ x29 . x29 ∈ x0 ⟶ ∀ x30 . x30 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x3 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x3 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x4 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x4 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x4 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x5 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x5 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x5 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x5 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x6 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x6 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x6 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x6 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x6 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x7 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x7 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x7 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x7 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x7 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x7 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x8 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x9 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x10 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x11 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x12 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x13 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x14 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x15 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x16 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x17 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x18 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x19 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x20 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x21 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x22 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x23 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x24 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x24 = x25 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x24 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x25 = x26 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x24 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x25 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x26 = x27 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x24 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x25 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x26 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x27 = x28 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x24 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x25 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x26 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x27 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x28 = x29 ⟶ ∀ x31 : ο . x31) ⟶ (x1 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x2 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x3 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x4 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x5 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x6 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x7 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x8 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x9 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x10 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x11 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x12 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x13 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x14 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x15 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x16 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x17 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x18 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x19 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x20 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x21 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x22 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x23 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x24 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x25 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x26 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x27 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x28 = x30 ⟶ ∀ x31 : ο . x31) ⟶ (x29 = x30 ⟶ ∀ x31 : ο . x31) ⟶ atleastp u30 x0 (proof)
Definition u31 := ordsucc u30
Theorem 1fc45.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ ∀ x29 . x29 ∈ x0 ⟶ ∀ x30 . x30 ∈ x0 ⟶ ∀ x31 . x31 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x3 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x3 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x4 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x4 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x4 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x5 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x5 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x5 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x5 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x6 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x6 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x6 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x6 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x6 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x7 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x7 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x7 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x7 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x7 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x7 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x8 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x9 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x10 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x11 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x12 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x13 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x14 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x15 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x16 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x17 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x18 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x19 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x20 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x21 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x22 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x23 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x24 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x25 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x25 = x26 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x25 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x26 = x27 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x25 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x26 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x27 = x28 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x25 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x26 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x27 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x28 = x29 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x25 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x26 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x27 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x28 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x29 = x30 ⟶ ∀ x32 : ο . x32) ⟶ (x1 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x2 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x3 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x4 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x5 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x6 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x7 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x8 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x9 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x10 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x11 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x12 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x13 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x14 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x15 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x16 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x17 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x18 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x19 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x20 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x21 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x22 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x23 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x24 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x25 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x26 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x27 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x28 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x29 = x31 ⟶ ∀ x32 : ο . x32) ⟶ (x30 = x31 ⟶ ∀ x32 : ο . x32) ⟶ atleastp u31 x0 (proof)
Definition u32 := ordsucc u31
Theorem 3c32a.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ ∀ x29 . x29 ∈ x0 ⟶ ∀ x30 . x30 ∈ x0 ⟶ ∀ x31 . x31 ∈ x0 ⟶ ∀ x32 . x32 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x3 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x3 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x4 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x4 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x4 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x5 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x5 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x5 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x5 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x6 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x6 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x6 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x6 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x6 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x7 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x7 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x7 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x7 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x7 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x7 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x8 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x9 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x10 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x11 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x12 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x13 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x14 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x15 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x16 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x17 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x18 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x19 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x20 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x21 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x22 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x23 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x24 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x25 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x26 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x26 = x27 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x26 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x27 = x28 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x26 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x27 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x28 = x29 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x26 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x27 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x28 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x29 = x30 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x26 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x27 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x28 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x29 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x30 = x31 ⟶ ∀ x33 : ο . x33) ⟶ (x1 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x2 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x3 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x4 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x5 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x6 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x7 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x8 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x9 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x10 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x11 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x12 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x13 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x14 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x15 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x16 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x17 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x18 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x19 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x20 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x21 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x22 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x23 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x24 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x25 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x26 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x27 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x28 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x29 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x30 = x32 ⟶ ∀ x33 : ο . x33) ⟶ (x31 = x32 ⟶ ∀ x33 : ο . x33) ⟶ atleastp u32 x0 (proof)
Definition u33 := ordsucc u32
Theorem cebd4.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ ∀ x29 . x29 ∈ x0 ⟶ ∀ x30 . x30 ∈ x0 ⟶ ∀ x31 . x31 ∈ x0 ⟶ ∀ x32 . x32 ∈ x0 ⟶ ∀ x33 . x33 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x3 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x3 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x4 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x4 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x4 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x5 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x5 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x5 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x5 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x6 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x6 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x6 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x6 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x6 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x7 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x7 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x7 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x7 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x7 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x7 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x8 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x9 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x10 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x11 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x12 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x13 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x14 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x15 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x16 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x17 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x18 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x19 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x20 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x21 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x22 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x23 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x24 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x25 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x26 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x27 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x27 = x28 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x27 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x28 = x29 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x27 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x28 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x29 = x30 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x27 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x28 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x29 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x30 = x31 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x27 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x28 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x29 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x30 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x31 = x32 ⟶ ∀ x34 : ο . x34) ⟶ (x1 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x2 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x3 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x4 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x5 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x6 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x7 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x8 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x9 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x10 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x11 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x12 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x13 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x14 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x15 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x16 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x17 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x18 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x19 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x20 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x21 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x22 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x23 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x24 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x25 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x26 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x27 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x28 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x29 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x30 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x31 = x33 ⟶ ∀ x34 : ο . x34) ⟶ (x32 = x33 ⟶ ∀ x34 : ο . x34) ⟶ atleastp u33 x0 (proof)
Definition u34 := ordsucc u33
Theorem 5e841.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ ∀ x28 . x28 ∈ x0 ⟶ ∀ x29 . x29 ∈ x0 ⟶ ∀ x30 . x30 ∈ x0 ⟶ ∀ x31 . x31 ∈ x0 ⟶ ∀ x32 . x32 ∈ x0 ⟶ ∀ x33 . x33 ∈ x0 ⟶ ∀ x34 . x34 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x3 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x3 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x4 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x4 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x4 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x5 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x5 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x5 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x5 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x6 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x6 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x6 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x6 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x6 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x7 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x7 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x7 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x7 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x7 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x7 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x8 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x9 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x10 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x11 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x12 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x13 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x14 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x15 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x16 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x17 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x18 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x19 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x20 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x21 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x22 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x23 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x24 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x25 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x26 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x27 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x28 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x28 = x29 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x28 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x29 = x30 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x28 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x29 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x30 = x31 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x28 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x29 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x30 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x31 = x32 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x28 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x29 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x30 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x31 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x32 = x33 ⟶ ∀ x35 : ο . x35) ⟶ (x1 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x2 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x3 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x4 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x5 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x6 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x7 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x8 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x9 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x10 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x11 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x12 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x13 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x14 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x15 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x16 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x17 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x18 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x19 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x20 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x21 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x22 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x23 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x24 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x25 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x26 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x27 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x28 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x29 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x30 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x31 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x32 = x34 ⟶ ∀ x35 : ο . x35) ⟶ (x33 = x34 ⟶ ∀ x35 : ο . x35) ⟶ atleastp u34 x0 (proof)