Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Apply explicit_Ring_minus_clos with
x0,
x1,
x3,
x4.
Apply explicit_Ring_with_id_Ring with
x0,
x1,
x2,
x3,
x4.
The subproof is completed by applying H0.