Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι be given.

Let x3 of type ι → ι 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 → ο be given.

Let x9 of type ι → ο be given.

Assume H0: ba600.. x0 x2 x4 x6 x8 = ba600.. x1 x3 x5 x7 x9.

Claim L1: x1 = f482f.. (ba600.. x0 x2 x4 x6 x8) 4a7ef..

Apply unknownprop_e7448b5c476bb2b70f2aefe5aec84016225ea14c810337d5001cce5e92e8db89 with ba600.. 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_ac8d22fd87c189cdacd13d3f0c153378837738a7b924ad85c44f7e425c8a48d2 with x0, x2, x4, x6, x8.

Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ x2 x10 = x3 x10, ∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10, ∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10, ∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10 leaving 5 subgoals.

The subproof is completed by applying L2.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Apply unknownprop_88e63d6cdf90bf93c994f9a6b0e16f10694883e8818e3fd72d85285868c644e2 with x0, x2, x4, x6, x8, x10, λ x11 x12 . x12 = x3 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.. 4a7ef..)) x10 = x3 x10.

Let x11 of type ι → ι → ο be given.

Apply unknownprop_88e63d6cdf90bf93c994f9a6b0e16f10694883e8818e3fd72d85285868c644e2 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_97d7c9d5b9bb60ba7a2844311849651ff06e66a5ae8f16d43ea2da057ba67c39 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_97d7c9d5b9bb60ba7a2844311849651ff06e66a5ae8f16d43ea2da057ba67c39 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_a6d0137186f1e561d60a1a8fa39f7c3f4fe5a479b40ac5eeda53dabb95cffae0 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_a6d0137186f1e561d60a1a8fa39f7c3f4fe5a479b40ac5eeda53dabb95cffae0 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_d4148c1b4ac1a18dbc2df899e073f18c4b0cf203c719db50a8acdd1f1ed34390 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x9 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.. (4ae4a.. 4a7ef..))))) x10 = x9 x10.

Let x11 of type ο → ο → ο be given.

Apply unknownprop_d4148c1b4ac1a18dbc2df899e073f18c4b0cf203c719db50a8acdd1f1ed34390 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.

The subproof is completed by applying L4.

■

Proofgold Proof