Let x0 of type ι → ι → ο be given.
Let x1 of type ι → ι be given.
Assume H1: ∀ x2 x3 . x0 x2 x3 ⟶ x1 x2 = x1 x3.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H4: x0 x2 x3.
Apply andER with
x0 x2 x2,
x2 = canonical_elt_def x0 x1 x2,
λ x4 x5 . x5 = x3 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply andER with
x0 x3 x3,
x3 = canonical_elt_def x0 x1 x3,
λ x4 x5 . canonical_elt_def x0 x1 x2 = x5 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply canonical_elt_def_eq with
x0,
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.