Let x0 of type ι → ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H3: x0 x1 x2.
Apply andER with
x0 x1 x1,
x1 = canonical_elt x0 x1,
λ x3 x4 . x4 = x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply andER with
x0 x2 x2,
x2 = canonical_elt x0 x2,
λ x3 x4 . canonical_elt x0 x1 = x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply canonical_elt_eq with
x0,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.