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 be given.
Apply minus_SNo_invol with
x2,
λ x4 x5 . add_SNo (add_SNo x0 (add_SNo x1 (minus_SNo x2))) (add_SNo x4 x3) = add_SNo x0 (add_SNo x1 x3) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply add_SNo_minus_SNo_prop3 with
x0,
x1,
minus_SNo x2,
x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with
x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.