Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type (ι → ο) → ο be given.

Let x3 of type (ι → ο) → ο be given.

Let x4 of type ι → ι be given.

Let x5 of type ι → ι be given.

Let x6 of type ι → ι → ο be given.

Let x7 of type ι → ι → ο be given.

Assume H0: 17e9f.. x0 x2 x4 x6 = 17e9f.. x1 x3 x5 x7.

Claim L1: x1 = f482f.. (17e9f.. x0 x2 x4 x6) 4a7ef..

Apply unknownprop_007f1795bb83120bb9478e51b93a2d161aedff1592fda9bcba82e18e62f285b7 with 17e9f.. x0 x2 x4 x6, x1, x3, x5, x7.

The subproof is completed by applying H0.

Claim L2: x0 = x1

Apply L1 with λ x8 x9 . x0 = x9.

The subproof is completed by applying unknownprop_a6aeec7577d8b45f51a1b4fa07acbb2f80ce2cce3db0917ad7941ddc11875166 with x0, x2, x4, x6.

Apply and4I with x0 = x1, ∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8, ∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x6 x8 x9 = x7 x8 x9 leaving 4 subgoals.

The subproof is completed by applying L2.

Let x8 of type ι → ο be given.

Assume H3: ∀ x9 . x8 x9 ⟶ prim1 x9 x0.

Apply unknownprop_d0c017880678fcd65ad99be7e828cd3a18ab65c5cb6e8cacc01cf0609a657630 with x0, x2, x4, x6, x8, λ x9 x10 : ο . x10 = x3 x8 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: ∀ x9 . x8 x9 ⟶ prim1 x9 x1

Apply L2 with λ x9 x10 . ∀ x11 . x8 x11 ⟶ prim1 x11 x9.

The subproof is completed by applying H3.

Apply H0 with λ x9 x10 . decode_c (f482f.. x10 (4ae4a.. 4a7ef..)) x8 = x3 x8.

Let x9 of type ο → ο → ο be given.

Apply unknownprop_d0c017880678fcd65ad99be7e828cd3a18ab65c5cb6e8cacc01cf0609a657630 with x1, x3, x5, x7, x8, λ x10 x11 : ο . x9 x11 x10.

The subproof is completed by applying L4.

Let x8 of type ι be given.

Assume H3: prim1 x8 x0.

Apply unknownprop_ceb24fa1059e011557ca4438b2dcc412c46fba0e11220c6e3b75388ad54ca8ce with x0, x2, x4, x6, x8, λ x9 x10 . x10 = x5 x8 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: prim1 x8 x1

Apply L2 with λ x9 x10 . prim1 x8 x9.

The subproof is completed by applying H3.

Apply H0 with λ x9 x10 . f482f.. (f482f.. x10 (4ae4a.. (4ae4a.. 4a7ef..))) x8 = x5 x8.

Let x9 of type ι → ι → ο be given.

Apply unknownprop_ceb24fa1059e011557ca4438b2dcc412c46fba0e11220c6e3b75388ad54ca8ce with x1, x3, x5, x7, x8, λ x10 x11 . x9 x11 x10.

The subproof is completed by applying L4.

Let x8 of type ι be given.

Assume H3: prim1 x8 x0.

Let x9 of type ι be given.

Assume H4: prim1 x9 x0.

Apply unknownprop_8cc962999b2979b6bcbb6e4634188c09a486b85cbb8d9eb0200122c4937499d8 with x0, x2, x4, x6, x8, x9, λ x10 x11 : ο . x11 = x7 x8 x9 leaving 3 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

Claim L5: prim1 x8 x1

Apply L2 with λ x10 x11 . prim1 x8 x10.

The subproof is completed by applying H3.

Claim L6: prim1 x9 x1

Apply L2 with λ x10 x11 . prim1 x9 x10.

The subproof is completed by applying H4.

Apply H0 with λ x10 x11 . 2b2e3.. (f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 x9 = x7 x8 x9.

Let x10 of type ο → ο → ο be given.

Apply unknownprop_8cc962999b2979b6bcbb6e4634188c09a486b85cbb8d9eb0200122c4937499d8 with x1, x3, x5, x7, x8, x9, λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

■

Proofgold Proof