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.

Let x8 of type ι be given.

Let x9 of type ι be given.

Assume H0: 363b9.. x0 x2 x4 x6 x8 = 363b9.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (363b9.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_6ef01a13f7c36ada7f185a4c58513cabf0184466a91ecc2ed500a4a9e77c4a8d with 363b9.. 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_02f0cac4c02e49ce0f7220dcca6577c4622316d6aa3d6f676c744b755a99d67c with x0, x2, x4, x6, x8.

Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11, ∀ 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 be given.

Assume H3: prim1 x10 x0.

Let x11 of type ι be given.

Assume H4: prim1 x11 x0.

Apply unknownprop_f9155e921425190d6d2642091acbb7921641a6733a0d0953d242b68d21270afb with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x3 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.. 4a7ef..)) x10 x11 = x3 x10 x11.

Let x12 of type ο → ο → ο be given.

Apply unknownprop_f9155e921425190d6d2642091acbb7921641a6733a0d0953d242b68d21270afb 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.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Apply unknownprop_21b1a3136d7ac4765bfbef5c658131adbcc6bdea00fe52ebe3624f8fdbeaff24 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . 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 . decode_p (f482f.. x12 (4ae4a.. (4ae4a.. 4a7ef..))) x10 = x5 x10.

Let x11 of type ο → ο → ο be given.

Apply unknownprop_21b1a3136d7ac4765bfbef5c658131adbcc6bdea00fe52ebe3624f8fdbeaff24 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_97f1f10357220f1f8df31ca2897a79c3e582eb7b3b7efe8780fee275c21d2908 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_97f1f10357220f1f8df31ca2897a79c3e582eb7b3b7efe8780fee275c21d2908 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

Apply unknownprop_686688eba3937d844c992740ce546d6832458df24b71cdd37efd735ee35fba33 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_686688eba3937d844c992740ce546d6832458df24b71cdd37efd735ee35fba33 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof