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 → ο be given.

Let x5 of type ι → ι → ο be given.

Let x6 of type ι be given.

Let x7 of type ι be given.

Assume H0: d8d01.. x0 x2 x4 x6 = d8d01.. x1 x3 x5 x7.

Claim L1: x1 = f482f.. (d8d01.. x0 x2 x4 x6) 4a7ef..

Apply unknownprop_9475f9db34348b67db100836248d4844693614e5a951b989e9f5043adf44fcda with d8d01.. 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_d754eaf2b0fb19fb3d886b32f1b60dbaa8db7ea48022e79931c69cf7717a6d38 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 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9, x6 = x7 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_1c403a64ca50b475d6bc7af7f90763f88ed5ce47216d11d62787136b399d2c54 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_1c403a64ca50b475d6bc7af7f90763f88ed5ce47216d11d62787136b399d2c54 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.

Let x9 of type ι be given.

Assume H4: prim1 x9 x0.

Apply unknownprop_b476b153a6360678b1439cc46f7117cebbfe735588ee20ff35fcd444ab0ae523 with x0, x2, x4, x6, x8, x9, λ x10 x11 : ο . x11 = x5 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.. 4a7ef..))) x8 x9 = x5 x8 x9.

Let x10 of type ο → ο → ο be given.

Apply unknownprop_b476b153a6360678b1439cc46f7117cebbfe735588ee20ff35fcd444ab0ae523 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.

Apply unknownprop_a619e6c9c650f9242f9eb8820c4a42d5f40f543a1d8fbf54862d930cf3bb5b27 with x0, x2, x4, x6, λ x8 x9 . x9 = x7.

Apply H0 with λ x8 x9 . f482f.. x9 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.

Let x8 of type ι → ι → ο be given.

The subproof is completed by applying unknownprop_a619e6c9c650f9242f9eb8820c4a42d5f40f543a1d8fbf54862d930cf3bb5b27 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.

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Proofgold Proof