Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι be given.
Assume H1: x2 ∈ x0.
Apply explicit_Group_inverse_prop with
x0,
x1,
x2,
x1 x2 (explicit_Group_inverse x0 x1 x2) = explicit_Group_identity x0 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.