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 → ο be given.

Let x7 of type ι → ο be given.

Assume H0: 30bff.. x0 x2 x4 x6 = 30bff.. x1 x3 x5 x7.

Claim L1: x1 = f482f.. (30bff.. x0 x2 x4 x6) 4a7ef..

Apply unknownprop_25c4dac4a776c072d901ea169792c5e2271203a3819326f00804b5204952155b with 30bff.. 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_53a1434582c46791d97bf0b29daf1e96260f65f75da341b82fe60b82f00728d7 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, ∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8 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_7708a5a648779c332bd616f6e4513a6548347153ed171f25a7c039b600789f31 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_7708a5a648779c332bd616f6e4513a6548347153ed171f25a7c039b600789f31 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_580e8f89400098eafc477e78627cca2cb91e5401e413a05dcb445fa113c00c84 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_580e8f89400098eafc477e78627cca2cb91e5401e413a05dcb445fa113c00c84 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.

Let x8 of type ι be given.

Assume H3: prim1 x8 x0.

Apply unknownprop_26c09a5fb4cb36f7b0ddea94b180a8c22b92587770fba43cdead9a6362679f2e with x0, x2, x4, x6, x8, λ x9 x10 : ο . x10 = x7 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 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 = x7 x8.

Let x9 of type ο → ο → ο be given.

Apply unknownprop_26c09a5fb4cb36f7b0ddea94b180a8c22b92587770fba43cdead9a6362679f2e with x1, x3, x5, x7, x8, λ x10 x11 : ο . x9 x11 x10.

The subproof is completed by applying L4.

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Proofgold Proof