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.

Assume H0: e0718.. x0 x2 x4 = e0718.. x1 x3 x5.

Claim L1: x1 = f482f.. (e0718.. x0 x2 x4) 4a7ef..

Apply unknownprop_1e110a2b0eac66e464fcd0049e51159c6573a7f238676ed96b2b7556f087fb8f with e0718.. x0 x2 x4, x1, x3, x5.

The subproof is completed by applying H0.

Claim L2: x0 = x1

Apply L1 with λ x6 x7 . x0 = x7.

The subproof is completed by applying unknownprop_c7497c326e0bcb75fa2cc505e6dafed2f342db0b83093fa52226d04b865b9a91 with x0, x2, x4.

Apply and3I with x0 = x1, ∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6, ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x6 x7 = x5 x6 x7 leaving 3 subgoals.

The subproof is completed by applying L2.

Let x6 of type ι → ο be given.

Assume H3: ∀ x7 . x6 x7 ⟶ prim1 x7 x0.

Apply unknownprop_71d4b3d2b3a5f29d2cd05a29c47b2f0fa1a64aff8b5bd681eeb78733ed987d9d with x0, x2, x4, x6, λ x7 x8 : ο . x8 = x3 x6 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: ∀ x7 . x6 x7 ⟶ prim1 x7 x1

Apply L2 with λ x7 x8 . ∀ x9 . x6 x9 ⟶ prim1 x9 x7.

The subproof is completed by applying H3.

Apply H0 with λ x7 x8 . decode_c (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.

Let x7 of type ο → ο → ο be given.

Apply unknownprop_71d4b3d2b3a5f29d2cd05a29c47b2f0fa1a64aff8b5bd681eeb78733ed987d9d with x1, x3, x5, x6, λ x8 x9 : ο . x7 x9 x8.

The subproof is completed by applying L4.

Let x6 of type ι be given.

Assume H3: prim1 x6 x0.

Let x7 of type ι be given.

Assume H4: prim1 x7 x0.

Apply unknownprop_b1715816bd75ab55604fa7666530ab99e6bf52403540cf592ed4c4fda9cb0db1 with x0, x2, x4, x6, x7, λ x8 x9 . x9 = x5 x6 x7 leaving 3 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

Claim L5: prim1 x6 x1

Apply L2 with λ x8 x9 . prim1 x6 x8.

The subproof is completed by applying H3.

Claim L6: prim1 x7 x1

Apply L2 with λ x8 x9 . prim1 x7 x8.

The subproof is completed by applying H4.

Apply H0 with λ x8 x9 . e3162.. (f482f.. x9 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 = x5 x6 x7.

Let x8 of type ι → ι → ο be given.

Apply unknownprop_b1715816bd75ab55604fa7666530ab99e6bf52403540cf592ed4c4fda9cb0db1 with x1, x3, x5, x6, x7, λ x9 x10 . x8 x10 x9 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

■

Proofgold Proof