Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ο be given.

Let x3 of type ι → ι → ο be given.

Let x4 of type ι → ι → ο be given.

Let x5 of type ι → ι → ο be given.

Let x6 of type ι → ο be given.

Let x7 of type ι → ο be given.

Assume H0: 3bbe6.. x0 x2 x4 x6 = 3bbe6.. x1 x3 x5 x7.

Claim L1: x1 = f482f.. (3bbe6.. x0 x2 x4 x6) 4a7ef..

Apply unknownprop_cab7d18ee12afc77da9afb2183f64425c49a92e7e1f4f32ed873b265c0925369 with 3bbe6.. 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_02c53fc08deb7f298911cf54bdb69a7e4b2fa803c595c3f8d58cfbe82a79bf16 with x0, x2, x4, x6.

Apply and4I with x0 = x1, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8 leaving 4 subgoals.

The subproof is completed by applying L2.

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_6f772c6da0aab5aece1637a76dcf223a881c459906c3f211b954b070367a1754 with x0, x2, x4, x6, x8, x9, λ x10 x11 : ο . x11 = x3 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 . 2b2e3.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.

Let x10 of type ο → ο → ο be given.

Apply unknownprop_6f772c6da0aab5aece1637a76dcf223a881c459906c3f211b954b070367a1754 with x1, x3, x5, x7, x8, x9, λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

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_dc4e78b47e6fae7cd7bf5581eed8695dd3f4aab5f5880b6ade2f67a2f2ca76f6 with x0, x2, x4, x6, x8, x9, λ x10 x11 : ο . 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 . 2b2e3.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.

Let x10 of type ο → ο → ο be given.

Apply unknownprop_dc4e78b47e6fae7cd7bf5581eed8695dd3f4aab5f5880b6ade2f67a2f2ca76f6 with x1, x3, x5, x7, x8, x9, λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.

The subproof is completed by applying L5.

The subproof is completed by applying L6.

Let x8 of type ι be given.

Assume H3: prim1 x8 x0.

Apply unknownprop_96bdc5d197cdc666ad511e997d68048ab86f4825b9fd33fe8b8c8464f3db7698 with x0, x2, x4, x6, x8, λ x9 x10 : ο . x10 = x7 x8 leaving 2 subgoals.

The subproof is completed by applying H3.

Claim L4: prim1 x8 x1

Apply L2 with λ x9 x10 . prim1 x8 x9.

The subproof is completed by applying H3.

Apply H0 with λ x9 x10 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 = x7 x8.

Let x9 of type ο → ο → ο be given.

Apply unknownprop_96bdc5d197cdc666ad511e997d68048ab86f4825b9fd33fe8b8c8464f3db7698 with x1, x3, x5, x7, x8, λ x10 x11 : ο . x9 x11 x10.

The subproof is completed by applying L4.

■

Proofgold Proof