Proofgold Asset

Definition Church17_perm_13_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12 := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x14 x15 x16 x17 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Definition Church17_p := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x6) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x7) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x8) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x9) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x10) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x11) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x12) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x13) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x15) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x18) ⟶ x1 x0
Known 51598.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x13)
Known 15dad.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x14)
Known 7e8b2.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x15)
Known 02267.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x16)
Known e70c8.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0)
Known 1b7f9.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x1)
Known 25b64.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x2)
Known 9e7eb.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x3)
Known 51a81.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4)
Known e224e.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x5)
Known 5d397.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6)
Known 3b0d1.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x7)
Known e7def.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x8)
Known a8b9a.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x9)
Known 4f699.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x10)
Known 712d3.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11)
Known d5e0f.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x12)
Theorem 7599a.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p (Church17_perm_13_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12 x0) (proof)
Definition TwoRamseyGraph_4_4_Church17 := λ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x2 x3 . x0 (x1 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2) (x1 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2) (x1 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3) (x1 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2) (x1 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3) (x1 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3) (x1 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3) (x1 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2) (x1 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2) (x1 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3 x3) (x1 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3 x3) (x1 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2 x3) (x1 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3 x2) (x1 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2 x3) (x1 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x2) (x1 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2) (x1 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x2 x3 x2 x2 x3)
Theorem 7d016.. : ∀ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p x1 ⟶ TwoRamseyGraph_4_4_Church17 x0 x1 = TwoRamseyGraph_4_4_Church17 (Church17_perm_13_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12 x0) (Church17_perm_13_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12 x1) (proof)
Definition Church17_perm_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13 := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x15 x16 x17 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14
Theorem 8d815.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p (Church17_perm_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13 x0) (proof)
Theorem 2b360.. : ∀ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p x1 ⟶ TwoRamseyGraph_4_4_Church17 x0 x1 = TwoRamseyGraph_4_4_Church17 (Church17_perm_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13 x0) (Church17_perm_14_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13 x1) (proof)
Definition Church17_perm_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14 := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x16 x17 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15
Theorem 3d0f9.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p (Church17_perm_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14 x0) (proof)
Theorem 0b046.. : ∀ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p x1 ⟶ TwoRamseyGraph_4_4_Church17 x0 x1 = TwoRamseyGraph_4_4_Church17 (Church17_perm_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14 x0) (Church17_perm_15_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14 x1) (proof)
Definition Church17_perm_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14_15 := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x0 x17 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16
Theorem 32363.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p (Church17_perm_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14_15 x0) (proof)
Theorem 339e5.. : ∀ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p x1 ⟶ TwoRamseyGraph_4_4_Church17 x0 x1 = TwoRamseyGraph_4_4_Church17 (Church17_perm_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14_15 x0) (Church17_perm_16_0_1_2_3_4_5_6_7_8_9_10_11_12_13_14_15 x1) (proof)