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.

Assume H0: e8b89.. x0 x2 x4 x6 = e8b89.. x1 x3 x5 x7.

Claim L1: x1 = f482f.. (e8b89.. x0 x2 x4 x6) 4a7ef..

Apply unknownprop_3d18c2c773a83713e325082dbf3bda43f9ab50529769d168c0efb5c302e0d5cf with e8b89.. 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_0e532d62b1ffeb2e44a653293314211bf6ef2f87c27f36efb1563be78fd78d6d with x0, x2, x4, x6.

Apply and4I with x0 = x1, ∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9, x6 = x7 leaving 4 subgoals.

The subproof is completed by applying L2.

Let x8 of type ι → ο be given.

Assume H3: ∀ x9 . x8 x9 ⟶ prim1 x9 x0.

Apply unknownprop_87bcd25fc3366287afa74e30e32811ff9f473a08c1b1dad134df5a6438372c7f with x0, x2, x4, x6, x8, λ x9 x10 : ο . x10 = x3 x8 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: ∀ x9 . x8 x9 ⟶ prim1 x9 x1

Apply L2 with λ x9 x10 . ∀ x11 . x8 x11 ⟶ prim1 x11 x9.

The subproof is completed by applying H3.

Apply H0 with λ x9 x10 . decode_c (f482f.. x10 (4ae4a.. 4a7ef..)) x8 = x3 x8.

Let x9 of type ο → ο → ο be given.

Apply unknownprop_87bcd25fc3366287afa74e30e32811ff9f473a08c1b1dad134df5a6438372c7f with x1, x3, x5, x7, x8, λ x10 x11 : ο . x9 x11 x10.

The subproof is completed by applying L4.

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_11a43fb112690babe480ed081c340e61eff9ede8136723ff028f6405ad595668 with x0, x2, x4, x6, x8, x9, λ x10 x11 . x11 = x5 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 . e3162.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.

Let x10 of type ι → ι → ο be given.

Apply unknownprop_11a43fb112690babe480ed081c340e61eff9ede8136723ff028f6405ad595668 with x1, x3, x5, x7, x8, x9, λ x11 x12 . x10 x12 x11 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

Apply unknownprop_461a5994de8b4df809b00ca38ec0a04acad276e10d8366f13b7e301477945ae4 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_461a5994de8b4df809b00ca38ec0a04acad276e10d8366f13b7e301477945ae4 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.

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Proofgold Proof