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.

Let x8 of type ι be given.

Let x9 of type ι be given.

Assume H0: fe7e3.. x0 x2 x4 x6 x8 = fe7e3.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (fe7e3.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_7bf622f5b680dccdb254a614f8b9f24a8eba45aeddbe91d06d85084c536e0096 with fe7e3.. 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_0cf25aee1aa3da57541ced65711a31bdf8c1adc2842aaacec0283988f600ba28 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, 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_bd7df01b1bb51569937528679c59d4ba358b10f67a8c2200468ec7fa888fb726 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_bd7df01b1bb51569937528679c59d4ba358b10f67a8c2200468ec7fa888fb726 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_b3896936979d3dfc36b30b98f712f7e9af8a0e1fec901b0aa1270247d172a448 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . 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 . 2b2e3.. (f482f.. x13 (4ae4a.. (4ae4a.. 4a7ef..))) x10 x11 = x5 x10 x11.

Let x12 of type ο → ο → ο be given.

Apply unknownprop_b3896936979d3dfc36b30b98f712f7e9af8a0e1fec901b0aa1270247d172a448 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 : ο . x12 x14 x13 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

Apply unknownprop_94d5d45a49954094229a693debff9e0992350d175dfdfc61f9a83c91eb555ae2 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_94d5d45a49954094229a693debff9e0992350d175dfdfc61f9a83c91eb555ae2 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

Apply unknownprop_efd5b0e4635a13150619341727a4e9f3237b474d633dc1b7cfc9d6140575d9f7 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_efd5b0e4635a13150619341727a4e9f3237b474d633dc1b7cfc9d6140575d9f7 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof