Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Apply unknownprop_90e0281ca50dd9937c4dc4598e4b18b763eeb528d21427cfd7d571699b566522 with
explicit_abelian,
x0,
x1.
Let x2 of type ι → ι → ι be given.
Assume H0:
∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = x2 x3 x4.
Let x3 of type ο → ο → ο be given.
Apply prop_ext with
explicit_abelian x0 x1,
explicit_abelian x0 x2,
λ x4 x5 : ο . x3 x5 x4.
Apply explicit_abelian_repindep with
x0,
x1,
x2.
The subproof is completed by applying H0.