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 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: 6b0a5.. x0 x2 x4 x6 x8 = 6b0a5.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (6b0a5.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_31b723a28399d35883e7c34db9a9ad0f68f2543f8c2a19a44c2c0a3a24fb1400 with 6b0a5.. 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_60e1285d2ccc72f95127634d66da7efc514376e8511cd196b24e4fbf48de2cda 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_08bd9c8319c4d506ca6d459977b52421ac002bdb8ef2e43b6d83455b6d159b6f 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_08bd9c8319c4d506ca6d459977b52421ac002bdb8ef2e43b6d83455b6d159b6f 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_c6695b92a4736f6489efede46708e2da8ebb268b4e2ac02e75aeb7464a9a61a7 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_c6695b92a4736f6489efede46708e2da8ebb268b4e2ac02e75aeb7464a9a61a7 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.

Apply unknownprop_389229da3772dfd44420288246db584f2385b5b60e9aee278525a0368b3d540c 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_389229da3772dfd44420288246db584f2385b5b60e9aee278525a0368b3d540c with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

Apply unknownprop_53e6d529605a4b5256fb5566fea600c12c5ce5c0a664882744edcf0b0e34ad81 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_53e6d529605a4b5256fb5566fea600c12c5ce5c0a664882744edcf0b0e34ad81 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof