Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ι → ι be given.

Apply unknownprop_90e0281ca50dd9937c4dc4598e4b18b763eeb528d21427cfd7d571699b566522 with λ x4 . λ x5 : ι → ι → ι . and (and (987b2.. x0 x2 = 987b2.. x4 x3) (4f2b4.. (987b2.. x4 x3))) (Subq x4 x1), x0, x2.

Let x4 of type ι → ι → ι be given.

Assume H0: ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = x4 x5 x6.

Let x5 of type ο → ο → ο be given.

Assume H1: x5 (and (and (987b2.. x0 x2 = 987b2.. x0 x3) (4f2b4.. (987b2.. x0 x3))) (Subq x0 x1)) (and (and (987b2.. x0 x2 = 987b2.. x0 x3) (4f2b4.. (987b2.. x0 x3))) (Subq x0 x1)).

The subproof is completed by applying H1.

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Proofgold Proof