Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply explicit_Group_inverse_rinv with
x0,
x1,
x2,
λ x4 x5 . x1 x2 x3 = x4 ⟶ x3 = explicit_Group_inverse x0 x1 x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply explicit_Group_lcancel with
x0,
x1,
x2,
x3,
explicit_Group_inverse x0 x1 x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply explicit_Group_inverse_in with
x0,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.