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Proofgold Proof

pf
Claim L0: ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0))) = x0
Let x0 of type ιιιιιιιιιιιιιιιιιι be given.
Assume H0: Church17_p x0.
Apply H0 with λ x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1))) = x1 leaving 17 subgoals.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x5))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x5).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x6))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x6).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x7))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x7).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x8))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x8).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x9))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x9).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x10))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x10).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x11))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x11).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x12))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x12).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x13))))) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x13).
The subproof is completed by applying H1.
Let x1 of type (ιιιιιιιιιιιιιιιιιι) → (ιιιιιιιιιιιιιιιιιι) → ο be given.
Assume H1: x1 ... ....
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Let x0 of type ι be given.
Assume H1: x0u16.
Claim L2: x0u17
Apply ordsuccI1 with u16, x0.
The subproof is completed by applying H1.
Apply unknownprop_f44342ed74648c23c8734d945bc8b2c1af5a9cb594ef51477e7844cb71f944f8 with x0.
The subproof is completed by applying L2.
Apply unknownprop_ab6e90e08cac98528b7a735e7b53e30c7970b36a1f906e2c6bc2d9edb6edf82f with u17_to_Church17 x0.
The subproof is completed by applying L3.
Apply unknownprop_ab6e90e08cac98528b7a735e7b53e30c7970b36a1f906e2c6bc2d9edb6edf82f with Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 x0).
The subproof is completed by applying L4.
Apply unknownprop_e902edb7e5c09f3911de6e6e7b47397939aa697886c0b6b7be0233b3765bcf65 with Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 x0), λ x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 (Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 (Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x2))))))) = x0 leaving 2 subgoals.
The subproof is completed by applying L4.
Apply unknownprop_e902edb7e5c09f3911de6e6e7b47397939aa697886c0b6b7be0233b3765bcf65 with Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 x0)), λ x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 (Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x2)))) = x0 leaving 2 subgoals.
The subproof is completed by applying L5.
Apply unknownprop_e902edb7e5c09f3911de6e6e7b47397939aa697886c0b6b7be0233b3765bcf65 with Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 x0))), λ x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x2) = x0 leaving 2 subgoals.
The subproof is completed by applying L6.
Apply L0 with u17_to_Church17 x0, λ x1 x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_to_u17 x2 = x0 leaving 2 subgoals.
The subproof is completed by applying L3.
Apply unknownprop_f0f6d6a5e0bad31ef814582844f5581ef6b06897d8b34d179a5f11d6a4ff9407 with x0.
The subproof is completed by applying L2.