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Proofgold Asset

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41b00573fa3deda6a8927c9b5b5cd89ef1cbc7b88dccd95efd21406bb22e39ab
asset hash
b74cb3a68ccf25166d118778cd5ff8f244b213d42038c82bdadbca56a276e84a
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18372
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aa678..
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doc published by Pr4zB..
Param andand : οοο
Definition ChurchNums_3x8_eq := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . and (x0 = x2) (x1 = x3)
Param notnot : οο
Definition ChurchNums_3x8_neq := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . not (ChurchNums_3x8_eq x0 x1 x2 x3)
Known andIandI : ∀ x0 x1 : ο . x0x1and x0 x1
Theorem f6916.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . x0 = x1x2 = x3ChurchNums_3x8_eq x0 x2 x1 x3 (proof)
Definition ChurchNums_8_perm_1_2_3_4_5_6_7_0 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x2 x3 x4 x5 x6 x7 x8 x1
Definition ChurchNums_8_perm_2_3_4_5_6_7_0_1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x3 x4 x5 x6 x7 x8 x1 x2
Definition ChurchNums_8_perm_3_4_5_6_7_0_1_2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x4 x5 x6 x7 x8 x1 x2 x3
Definition ChurchNums_8_perm_4_5_6_7_0_1_2_3 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x5 x6 x7 x8 x1 x2 x3 x4
Definition ChurchNums_8_perm_5_6_7_0_1_2_3_4 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x6 x7 x8 x1 x2 x3 x4 x5
Definition ChurchNums_8_perm_6_7_0_1_2_3_4_5 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x7 x8 x1 x2 x3 x4 x5 x6
Definition ChurchNums_8_perm_7_0_1_2_3_4_5_6 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 : (ι → ι)ι → ι . x0 x8 x1 x2 x3 x4 x5 x6 x7
Theorem accc4.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_1_2_3_4_5_6_7_0 (ChurchNums_8_perm_7_0_1_2_3_4_5_6 x0) = x0 (proof)
Theorem 13c67.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_2_3_4_5_6_7_0_1 (ChurchNums_8_perm_6_7_0_1_2_3_4_5 x0) = x0 (proof)
Theorem d720a.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_3_4_5_6_7_0_1_2 (ChurchNums_8_perm_5_6_7_0_1_2_3_4 x0) = x0 (proof)
Theorem 5a925.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_4_5_6_7_0_1_2_3 (ChurchNums_8_perm_4_5_6_7_0_1_2_3 x0) = x0 (proof)
Theorem 44285.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_5_6_7_0_1_2_3_4 (ChurchNums_8_perm_3_4_5_6_7_0_1_2 x0) = x0 (proof)
Theorem abce4.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_6_7_0_1_2_3_4_5 (ChurchNums_8_perm_2_3_4_5_6_7_0_1 x0) = x0 (proof)
Theorem 06461.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8_perm_7_0_1_2_3_4_5_6 (ChurchNums_8_perm_1_2_3_4_5_6_7_0 x0) = x0 (proof)
Definition ChurchNums_8x3_lt1_id_ge1_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2)
Definition ChurchNums_8x3_lt2_id_ge2_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2)
Definition ChurchNums_8x3_to_3_lt3_id_ge3_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2)
Definition ChurchNums_8x3_to_3_lt4_id_ge4_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2)
Definition ChurchNums_8x3_to_3_lt5_id_ge5_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x3 x4 x2) (x1 x3 x4 x2) (x1 x3 x4 x2)
Definition ChurchNums_8x3_to_3_lt6_id_ge6_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x3 x4 x2) (x1 x3 x4 x2)
Definition ChurchNums_8x3_to_3_lt7_id_ge7_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x3 x4 x2)
Definition ChurchNums_8x3_lt1_id_ge1_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3)
Definition ChurchNums_8x3_lt2_id_ge2_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3)
Definition ChurchNums_8x3_lt3_id_ge3_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3)
Definition ChurchNums_8x3_lt4_id_ge4_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3)
Definition ChurchNums_8x3_lt5_id_ge5_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x4 x2 x3) (x1 x4 x2 x3) (x1 x4 x2 x3)
Definition ChurchNums_8x3_lt6_id_ge6_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x4 x2 x3) (x1 x4 x2 x3)
Definition ChurchNums_8x3_lt7_id_ge7_rot1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x2 x3 x4) (x1 x4 x2 x3)
Definition ChurchNum_3ary_proj_p := λ x0 : ((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) → ο . x1 (λ x2 x3 x4 : (ι → ι)ι → ι . x2)x1 (λ x2 x3 x4 : (ι → ι)ι → ι . x3)x1 (λ x2 x3 x4 : (ι → ι)ι → ι . x4)x1 x0
Definition ChurchNum_8ary_proj_p := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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)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 : (ι → ι)ι → ι . x2)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x3)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x4)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x5)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x6)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x7)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x8)x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 : (ι → ι)ι → ι . x9)x1 x0
Theorem cef55.. : ChurchNum_3ary_proj_p (λ x0 x1 x2 : (ι → ι)ι → ι . x0) (proof)
Theorem 18961.. : ChurchNum_3ary_proj_p (λ x0 x1 x2 : (ι → ι)ι → ι . x1) (proof)
Theorem a5963.. : ChurchNum_3ary_proj_p (λ x0 x1 x2 : (ι → ι)ι → ι . x2) (proof)
Theorem 208f3.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x0) (proof)
Theorem ef1ab.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x1) (proof)
Theorem e5caa.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x2) (proof)
Theorem 446d8.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x3) (proof)
Theorem 3a83b.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x4) (proof)
Theorem 0ab9f.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x5) (proof)
Theorem 94187.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x6) (proof)
Theorem 7734d.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x7) (proof)
Theorem 081ec.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p (λ x1 x2 x3 : (ι → ι)ι → ι . x0 x2 x3 x1) (proof)
Theorem d5994.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p (λ x1 x2 x3 : (ι → ι)ι → ι . x0 x3 x1 x2) (proof)
Theorem b0f0d.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt1_id_ge1_rot2 x0 x1) (proof)
Theorem 16e4b.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt2_id_ge2_rot2 x0 x1) (proof)
Theorem ec90a.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_to_3_lt3_id_ge3_rot2 x0 x1) (proof)
Theorem 24233.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_to_3_lt4_id_ge4_rot2 x0 x1) (proof)
Theorem 7b754.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_to_3_lt5_id_ge5_rot2 x0 x1) (proof)
Theorem 2f553.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_to_3_lt6_id_ge6_rot2 x0 x1) (proof)
Theorem 1aa1c.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_to_3_lt7_id_ge7_rot2 x0 x1) (proof)
Theorem 0bfaf.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt1_id_ge1_rot1 x0 x1) (proof)
Theorem 1d5ae.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt2_id_ge2_rot1 x0 x1) (proof)
Theorem f7f04.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt3_id_ge3_rot1 x0 x1) (proof)
Theorem b68fb.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt4_id_ge4_rot1 x0 x1) (proof)
Theorem a776d.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt5_id_ge5_rot1 x0 x1) (proof)
Theorem 6c736.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt6_id_ge6_rot1 x0 x1) (proof)
Theorem f8e90.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)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 . ChurchNum_8ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_8x3_lt7_id_ge7_rot1 x0 x1) (proof)
Theorem c2824.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt1_id_ge1_rot2 x0 (ChurchNums_8x3_lt1_id_ge1_rot1 x0 x1) = x1 (proof)
Theorem 0e9d3.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt2_id_ge2_rot2 x0 (ChurchNums_8x3_lt2_id_ge2_rot1 x0 x1) = x1 (proof)
Theorem 92519.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_to_3_lt3_id_ge3_rot2 x0 (ChurchNums_8x3_lt3_id_ge3_rot1 x0 x1) = x1 (proof)
Theorem ad374.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_to_3_lt4_id_ge4_rot2 x0 (ChurchNums_8x3_lt4_id_ge4_rot1 x0 x1) = x1 (proof)
Theorem a48ad.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_to_3_lt5_id_ge5_rot2 x0 (ChurchNums_8x3_lt5_id_ge5_rot1 x0 x1) = x1 (proof)
Theorem fa851.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_to_3_lt6_id_ge6_rot2 x0 (ChurchNums_8x3_lt6_id_ge6_rot1 x0 x1) = x1 (proof)
Theorem dfbcd.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_to_3_lt7_id_ge7_rot2 x0 (ChurchNums_8x3_lt7_id_ge7_rot1 x0 x1) = x1 (proof)
Theorem b782a.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt1_id_ge1_rot1 x0 (ChurchNums_8x3_lt1_id_ge1_rot2 x0 x1) = x1 (proof)
Theorem 53c9b.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt2_id_ge2_rot1 x0 (ChurchNums_8x3_lt2_id_ge2_rot2 x0 x1) = x1 (proof)
Theorem 28253.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt3_id_ge3_rot1 x0 (ChurchNums_8x3_to_3_lt3_id_ge3_rot2 x0 x1) = x1 (proof)
Theorem 49e33.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt4_id_ge4_rot1 x0 (ChurchNums_8x3_to_3_lt4_id_ge4_rot2 x0 x1) = x1 (proof)
Theorem b1cc9.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt5_id_ge5_rot1 x0 (ChurchNums_8x3_to_3_lt5_id_ge5_rot2 x0 x1) = x1 (proof)
Theorem 8922d.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt6_id_ge6_rot1 x0 (ChurchNums_8x3_to_3_lt6_id_ge6_rot2 x0 x1) = x1 (proof)
Theorem e57bb.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_8x3_lt7_id_ge7_rot1 x0 (ChurchNums_8x3_to_3_lt7_id_ge7_rot2 x0 x1) = x1 (proof)
Theorem 4ac5f.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_1_2_3_4_5_6_7_0 x0) (proof)
Theorem c5de4.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_2_3_4_5_6_7_0_1 x0) (proof)
Theorem eaaf4.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_3_4_5_6_7_0_1_2 x0) (proof)
Theorem dac10.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_4_5_6_7_0_1_2_3 x0) (proof)
Theorem eed30.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_5_6_7_0_1_2_3_4 x0) (proof)
Theorem a5ec6.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_6_7_0_1_2_3_4_5 x0) (proof)
Theorem e1672.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_7_0_1_2_3_4_5_6 x0) (proof)
Definition TwoRamseyGraph_4_5_24_ChurchNums_3x8 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x4 . x0 (x1 (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)))) (x1 (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ 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. x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)))) (x1 (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)))) (λ x5 . x4)
Theorem f60cd.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x2 x1 x3 = TwoRamseyGraph_4_5_24_ChurchNums_3x8 x1 x3 x0 x2 (proof)
Param ordsuccordsucc : ιι
Definition TwoRamseyGraph_4_5_24 := λ x0 x1 . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x4 x5 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x2ChurchNum_3ary_proj_p x3ChurchNum_8ary_proj_p x4ChurchNum_8ary_proj_p x5x0 = x2 (λ x7 : ι → ι . λ x8 . x8) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 x8)))))))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 x8)))))))))))))))) ordsucc (x4 (λ x7 : ι → ι . λ x8 . x8) (λ x7 : ι → ι . x7) (λ x7 : ι → ι . λ x8 . x7 (x7 x8)) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 x8))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 x8)))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 x8))))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 x8)))))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 (x7 x8))))))) ordsucc 0)x1 = x3 (λ x7 : ι → ι . λ x8 . x8) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 x8)))))))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 (x7 x8)))))))))))))))) ordsucc (x5 (λ x7 : ι → ι . λ x8 . x8) (λ x7 : ι → ι . x7) (λ x7 : ι → ι . λ x8 . x7 (x7 x8)) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 x8))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 x8)))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 x8))))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 x8)))))) (λ x7 : ι → ι . λ x8 . x7 (x7 (x7 (x7 (x7 (x7 (x7 x8))))))) ordsucc 0)TwoRamseyGraph_4_5_24_ChurchNums_3x8 x2 x4 x3 x5 = λ x7 x8 . x7
Theorem 9303b.. : ∀ x0 x1 . TwoRamseyGraph_4_5_24 x0 x1TwoRamseyGraph_4_5_24 x1 x0 (proof)