Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ο be given.

Let x3 of type ι → ι → ο be given.

Let x4 of type ι → ο be given.

Let x5 of type ι → ο be given.

Let x6 of type ι be given.

Let x7 of type ι be given.

Assume H0: e4ab3.. x0 x2 x4 x6 = e4ab3.. x1 x3 x5 x7.

Claim L1: x1 = f482f.. (e4ab3.. x0 x2 x4 x6) 4a7ef..

Apply unknownprop_8e32916ae8c28f2ebe0d52c71f849e46ce2048516ac6d4d8cb2040b18b6dbdb9 with e4ab3.. 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_c9152796840c410a62ce994b0c774a129f2dd25c2fc66915b7cfb0ba0dbb18d5 with x0, x2, x4, x6.

Apply and4I with x0 = x1, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8, x6 = x7 leaving 4 subgoals.

The subproof is completed by applying L2.

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_205a8e50402a6e8cbed05df2f8d749d02992f9b6d93a4504b74ffeb148417bea with x0, x2, x4, x6, x8, x9, λ x10 x11 : ο . x11 = x3 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.. 4a7ef..)) x8 x9 = x3 x8 x9.

Let x10 of type ο → ο → ο be given.

Apply unknownprop_205a8e50402a6e8cbed05df2f8d749d02992f9b6d93a4504b74ffeb148417bea 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_4e78cf47ffbdfabaacc771ac6807e8dd02581e54f1697892cd92679610639207 with x0, x2, x4, x6, x8, λ x9 x10 : ο . x10 = x5 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.. 4a7ef..))) x8 = x5 x8.

Let x9 of type ο → ο → ο be given.

Apply unknownprop_4e78cf47ffbdfabaacc771ac6807e8dd02581e54f1697892cd92679610639207 with x1, x3, x5, x7, x8, λ x10 x11 : ο . x9 x11 x10.

The subproof is completed by applying L4.

Apply unknownprop_bde2160fde0a8614929b4c96f813dfa1b3a6ed023b65cf1a27e4ace755a947cd with x0, x2, x4, x6, λ x8 x9 . x9 = x7.

Apply H0 with λ x8 x9 . f482f.. x9 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.

Let x8 of type ι → ι → ο be given.

The subproof is completed by applying unknownprop_bde2160fde0a8614929b4c96f813dfa1b3a6ed023b65cf1a27e4ace755a947cd with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.

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Proofgold Proof