Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Let x3 of type ι be given.

Assume H0: 80242.. x1.

Assume H1: 80242.. x2.

Assume H2: 80242.. x3.

set y4 to be bc82c.. x0 (bc82c.. x1 (bc82c.. x2 x3))

set y5 to be bc82c.. x1 (bc82c.. x3 (bc82c.. x2 y4))

Claim L3: ∀ x6 : ι → ο . x6 y5 ⟶ x6 y4

Let x6 of type ι → ο be given.

Assume H3: x6 (bc82c.. x2 (bc82c.. y4 (bc82c.. x3 y5))).

set y7 to be λ x7 . x6

Apply unknownprop_3341a621e79d3f9f700c2a0db134f89ed08835f1d46a262ace9da8089fc62fd8 with x3, y4, y5, λ x8 x9 . y7 (bc82c.. x2 x8) (bc82c.. x2 x9) leaving 4 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

The subproof is completed by applying H2.

The subproof is completed by applying H3.

Let x6 of type ι → ι → ο be given.

Apply L3 with λ x7 . x6 x7 y5 ⟶ x6 y5 x7.

Assume H4: x6 y5 y5.

The subproof is completed by applying H4.

■

Proofgold Proof