Let x0 of type ι be given.

Let x1 of type ι → ι be given.

Let x2 of type ι be given.

Assume H0: prim1 x2 x0.

Apply unknownprop_0e196a42801a85c375f9ddf24d12703e84f3cb2a30f0d38cf82a793a3f90c693 with x0, x1, x1 x2, prim1 (x1 x2) (94f9e.. x0 (λ x3 . x1 x3)).

Assume H1: prim1 (x1 x2) (94f9e.. x0 x1) ⟶ ∃ x3 . and (prim1 x3 x0) (x1 x2 = x1 x3).

Assume H2: (∃ x3 . and (prim1 x3 x0) (x1 x2 = x1 x3)) ⟶ prim1 (x1 x2) (94f9e.. x0 x1).

Apply H2.

Let x3 of type ο be given.

Assume H3: ∀ x4 . and (prim1 x4 x0) (x1 x2 = x1 x4) ⟶ x3.

Apply H3 with x2.

Apply andI with prim1 x2 x0, x1 x2 = x1 x2 leaving 2 subgoals.

The subproof is completed by applying H0.

Let x4 of type ι → ι → ο be given.

Assume H4: x4 (x1 x2) (x1 x2).

The subproof is completed by applying H4.

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Proofgold Proof