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 → 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: bebf6.. x0 x2 x4 x6 x8 = bebf6.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (bebf6.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_757d9f4e5c843e1937e6e708cf97ede29dd7c813bcc43b4764db9072b8f0e009 with bebf6.. x0 ... ... ... ..., ..., ..., ..., ..., ....

...

Claim L2: x0 = x1

Apply L1 with λ x10 x11 . x0 = x11.

The subproof is completed by applying unknownprop_65cce1600a86bdb4fcc47c3f21cd540289b2d8a67dba9d2cfdb16c7b60cd3592 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11, ∀ 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_893520f3075c4d3a8ba22723b37a813951891a352483f9ee1c79192185721ed8 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_893520f3075c4d3a8ba22723b37a813951891a352483f9ee1c79192185721ed8 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.

Let x11 of type ι be given.

Assume H4: prim1 x11 x0.

Apply unknownprop_d00271e3409a7f60fd60ced864a095054ad7fb1dd9954a22fb8f485fbf2f84a4 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x5 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 . e3162.. (f482f.. x13 (4ae4a.. (4ae4a.. 4a7ef..))) x10 x11 = x5 x10 x11.

Let x12 of type ι → ι → ο be given.

Apply unknownprop_d00271e3409a7f60fd60ced864a095054ad7fb1dd9954a22fb8f485fbf2f84a4 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 . 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_8472672de8e4a6002250f4bca01a91b0df686dd5f362cb55afa19360ce15f05d 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_8472672de8e4a6002250f4bca01a91b0df686dd5f362cb55afa19360ce15f05d with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

Apply unknownprop_d541830b9bb76016fdfd9d4a39b99cfc03581aed7733587f376a6613a3d27e18 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_d541830b9bb76016fdfd9d4a39b99cfc03581aed7733587f376a6613a3d27e18 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof