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 → ι be given.

Let x5 of type ι → ι → ι be given.

Let x6 of type ι → ι be given.

Let x7 of type ι → ι be given.

Let x8 of type ι be given.

Let x9 of type ι be given.

Assume H0: a0d6b.. x0 x2 x4 x6 x8 = a0d6b.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (a0d6b.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_7ee1fe2452c751cda0289012076c1d173345076630775d01990c0c3f6441ec59 with a0d6b.. x0 ... ... ... ..., ..., ..., ..., ..., ....

...

Claim L2: x0 = x1

Apply L1 with λ x10 x11 . x0 = x11.

The subproof is completed by applying unknownprop_d5d88045d2cfa871239dc0f1e390ae7aad937199aca4b3216cd4e5cd7c86d8d5 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10, 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_ecd6510e2ea849e255f555706958929b3559e720426f1ab5e91b63fe3bbcb48d 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_ecd6510e2ea849e255f555706958929b3559e720426f1ab5e91b63fe3bbcb48d 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.

Let x11 of type ι be given.

Assume H4: prim1 x11 x0.

Apply unknownprop_f12f7eba5a79ad85ae8a6cc5a5b5a8013a57736e67b9aa5321018e0e7b5df2d6 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x5 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.. (4ae4a.. 4a7ef..))) x10 x11 = x5 x10 x11.

Let x12 of type ι → ι → ο be given.

Apply unknownprop_f12f7eba5a79ad85ae8a6cc5a5b5a8013a57736e67b9aa5321018e0e7b5df2d6 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_f3e60ee4a0214596c25a0fad5a25b3a8957384d8d8bfef9c8da5b0ae2b9d5247 with x0, x2, x4, x6, x8, x10, λ x11 x12 . x12 = x7 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 . f482f.. (f482f.. x12 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 = x7 x10.

Let x11 of type ι → ι → ο be given.

Apply unknownprop_f3e60ee4a0214596c25a0fad5a25b3a8957384d8d8bfef9c8da5b0ae2b9d5247 with x1, x3, x5, x7, x9, x10, λ x12 x13 . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_56d1b6655785b5368e2fb8c8e37775ae7ae30eb70563dd7941f7c2068a470e39 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_56d1b6655785b5368e2fb8c8e37775ae7ae30eb70563dd7941f7c2068a470e39 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof