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 → 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: 98165.. x0 x2 x4 x6 x8 = 98165.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (98165.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_fa060beed5004aeaf903e37baa1eb6cd4f20ae72d2b2b92763eab92a49d0ec7b with 98165.. 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_4446df303565862bba749bc3b3796f1833a33e7c7081a067192379a7c1d64c04 with x0, x2, x4, x6, x8.

Apply and5I with x0 = x1, ∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10, ∀ 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 → ο be given.

Assume H3: ∀ x11 . x10 x11 ⟶ prim1 x11 x0.

Apply unknownprop_942aa5d8b4e5ee282c21621bfe762ed5c1586eafb0f3bffa1e4e44c94b9c7e56 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x3 x10 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: ∀ x11 . x10 x11 ⟶ prim1 x11 x1

Apply L2 with λ x11 x12 . ∀ x13 . x10 x13 ⟶ prim1 x13 x11.

The subproof is completed by applying H3.

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

Let x11 of type ο → ο → ο be given.

Apply unknownprop_942aa5d8b4e5ee282c21621bfe762ed5c1586eafb0f3bffa1e4e44c94b9c7e56 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Apply unknownprop_70e7ccfbe2faf29b33294498f617cecc17544a6c5bca88f848370cd4de95ea43 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_70e7ccfbe2faf29b33294498f617cecc17544a6c5bca88f848370cd4de95ea43 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_f69656ed661027e20424f9892bdd76c006ab20fc5d7ad4c2ac380a23f2b07cf7 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_f69656ed661027e20424f9892bdd76c006ab20fc5d7ad4c2ac380a23f2b07cf7 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

Apply unknownprop_12482a7f3b6d06d949ae831c83e57b0424853f81e2459db4981aead803933efa 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_12482a7f3b6d06d949ae831c83e57b0424853f81e2459db4981aead803933efa with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

■

Proofgold Proof