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 → ο be given.

Let x7 of type ι → ο be given.

Let x8 of type ι be given.

Let x9 of type ι be given.

Assume H0: 2e40c.. x0 x2 x4 x6 x8 = 2e40c.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (2e40c.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_f50dd06fbf119506e751474ab9fe55f5c76bee0d70f414d468384ad9cfaf2c39 with 2e40c.. 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_5091b23ace185de1439c9993ecf5d34c3889f1adbf8fc4314bc1ac1fed4972cf 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, ∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10, 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_a13b376ead7440cfb8068d51b0fc26b8bee9b2fd7f0c4983ba28169597604378 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_a13b376ead7440cfb8068d51b0fc26b8bee9b2fd7f0c4983ba28169597604378 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_08751a2182e392d896e3e3f4a36e5bf5e3e32f0eec6892705c231ffefc7cc6f0 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_08751a2182e392d896e3e3f4a36e5bf5e3e32f0eec6892705c231ffefc7cc6f0 with x1, x3, x5, x7, x9, x10, λ x12 x13 . x11 x13 x12.

The subproof is completed by applying L4.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Apply unknownprop_04e910d1de9e4552e9264adbcc682f73b876009ed78e0a9d5f152658b15ea3ba with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x7 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.. (4ae4a.. 4a7ef..)))) x10 = x7 x10.

Let x11 of type ο → ο → ο be given.

Apply unknownprop_04e910d1de9e4552e9264adbcc682f73b876009ed78e0a9d5f152658b15ea3ba with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_3ab7806cf0ff3d8bee638a9c7ebd5be410ba51ca429236345648ab7856c58a31 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_3ab7806cf0ff3d8bee638a9c7ebd5be410ba51ca429236345648ab7856c58a31 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof