Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ι → ι be given.

Let x4 of type ι → ο be given.

Let x5 of type ι → ο be given.

Let x6 of type ι be given.

Let x7 of type ι be given.

Let x8 of type ι be given.

Let x9 of type ι be given.

Assume H0: 59e44.. x0 x2 x4 x6 x8 = 59e44.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (59e44.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_70974f21707c4c0be2a461d7dbe042f6d8b75701c5008d9bf526e1b362d7a6a8 with 59e44.. x0 x2 x4 x6 x8, x1, x3, x5, x7, x9.

The subproof is completed by applying H0.

Claim L2: x0 = x1

Apply L1 with λ x10 x11 . x0 = x11.

The subproof is completed by applying unknownprop_a896d9879197a251fd7a12d69d8f360e5a92ebd292b2039bc93c32a66d0d6a96 with x0, x2, x4, x6, x8.

Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10, x6 = x7, x8 = x9 leaving 5 subgoals.

The subproof is completed by applying L2.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Let x11 of type ι be given.

Assume H4: prim1 x11 x0.

Apply unknownprop_35ac3343ba9f77f7330834114c550d4f16a9416ec06da8727722cee6becd4b4b with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x3 x10 x11 leaving 3 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

Claim L5: prim1 x10 x1

Apply L2 with λ x12 x13 . prim1 x10 x12.

The subproof is completed by applying H3.

Claim L6: prim1 x11 x1

Apply L2 with λ x12 x13 . prim1 x11 x12.

The subproof is completed by applying H4.

Apply H0 with λ x12 x13 . e3162.. (f482f.. x13 (4ae4a.. 4a7ef..)) x10 x11 = x3 x10 x11.

Let x12 of type ι → ι → ο be given.

Apply unknownprop_35ac3343ba9f77f7330834114c550d4f16a9416ec06da8727722cee6becd4b4b with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 . x12 x14 x13 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Apply unknownprop_09b21d8dbc48acba4ab8ef75bef8cf3254732bf9b8ee7b34ce4b2f32219944c3 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x5 x10 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: prim1 x10 x1

Apply L2 with λ x11 x12 . prim1 x10 x11.

The subproof is completed by applying H3.

Apply H0 with λ x11 x12 . decode_p (f482f.. x12 (4ae4a.. (4ae4a.. 4a7ef..))) x10 = x5 x10.

Let x11 of type ο → ο → ο be given.

Apply unknownprop_09b21d8dbc48acba4ab8ef75bef8cf3254732bf9b8ee7b34ce4b2f32219944c3 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_b2ff742e5629d24773381d0c70489e2e61d08f0a79b04e01904340003f191669 with x0, x2, x4, x6, x8, λ x10 x11 . x11 = x7.

Apply H0 with λ x10 x11 . f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.

Let x10 of type ι → ι → ο be given.

The subproof is completed by applying unknownprop_b2ff742e5629d24773381d0c70489e2e61d08f0a79b04e01904340003f191669 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

Apply unknownprop_cc70c9bfee05595139583a70a5077f4fab54212eeff0ace2bed75137e8c815be with x0, x2, x4, x6, x8, λ x10 x11 . x11 = x9.

Apply H0 with λ x10 x11 . f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x9.

Let x10 of type ι → ι → ο be given.

The subproof is completed by applying unknownprop_cc70c9bfee05595139583a70a5077f4fab54212eeff0ace2bed75137e8c815be with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof