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 be given.

Let x5 of type 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: 9d1fa.. x0 x2 x4 x6 x8 = 9d1fa.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (9d1fa.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_127904fec938a7f1c936b8220f143e9533d99ab54fefedd3aa937120ef6871c3 with 9d1fa.. 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_ed879a1dc003d9dcda0fdd2a2371eb92b77af1279f9917314fa3f01894ce3757 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_ea899678a937705a7509f2680383328fbc10c85ad26dd7c86f64b98aa28ee45f 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_ea899678a937705a7509f2680383328fbc10c85ad26dd7c86f64b98aa28ee45f 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_be48fd709323ffb96390a7b0a71dc73ab2165167fcff5538774858520232129f with x0, x2, x4, x6, x8, x10, λ x11 x12 . 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 . f482f.. (f482f.. x12 (4ae4a.. (4ae4a.. 4a7ef..))) x10 = x5 x10.

Let x11 of type ι → ι → ο be given.

Apply unknownprop_be48fd709323ffb96390a7b0a71dc73ab2165167fcff5538774858520232129f with x1, x3, x5, x7, x9, x10, λ x12 x13 . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_906b3495dc8cad94a6832c3cad07d8420e31e10346f24f30ac2c3a56d46d3e6a 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_906b3495dc8cad94a6832c3cad07d8420e31e10346f24f30ac2c3a56d46d3e6a with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

Apply unknownprop_6c3015699a85498856ba7ff7ec972259523976c85f0e2ad099f01a854acaea98 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_6c3015699a85498856ba7ff7ec972259523976c85f0e2ad099f01a854acaea98 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof