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 → ι → ο be given.

Let x7 of type ι → ι → ο be given.

Let x8 of type ι be given.

Let x9 of type ι be given.

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

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

Apply unknownprop_af6730e563e1a5cb9f35c3ffc6617d8ef348f3d27a27d705dbcd1410a7ca3d04 with 2cece.. 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_9c00f8a6468cbf26c7aa2fedf6b7ba6c24299a59bc94ead9a21a4122dc16f1bf 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11, x8 = x9 leaving 5 subgoals.

The subproof is completed by applying L2.

Let x10 of type ι be given.

Assume H3: prim1 x10 x0.

Apply unknownprop_c437c083995ca4c7d24f794797f46eebcc8e35fd673d72fa52431b29b930e70f 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_c437c083995ca4c7d24f794797f46eebcc8e35fd673d72fa52431b29b930e70f 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_48073b86f4b74bfcd3316dc47dc2e744f1fc1f2567c61579b27dbc9468d39401 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_48073b86f4b74bfcd3316dc47dc2e744f1fc1f2567c61579b27dbc9468d39401 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.

Let x11 of type ι be given.

Assume H4: prim1 x11 x0.

Apply unknownprop_64ae2dc1960077d9e9f005b67cd30a8fa340c12fc7ca4dacd26c87457b1d6adf with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x7 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.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 x11 = x7 x10 x11.

Let x12 of type ο → ο → ο be given.

Apply unknownprop_64ae2dc1960077d9e9f005b67cd30a8fa340c12fc7ca4dacd26c87457b1d6adf 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.

Apply unknownprop_e58b74dbd4f3e13e2978ca5351e448c7d44f0c599ffbc5b020aac1e953a0f879 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_e58b74dbd4f3e13e2978ca5351e448c7d44f0c599ffbc5b020aac1e953a0f879 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.

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Proofgold Proof