Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply SNo_minus_SNo with
x0.
The subproof is completed by applying H0.
Apply add_SNo_assoc with
minus_SNo x0,
x0,
x1,
λ x3 x4 . x4 = x1 leaving 4 subgoals.
The subproof is completed by applying L4.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_minus_SNo_linv with
x0,
λ x3 x4 . add_SNo x4 x1 = x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply add_SNo_0L with
x1.
The subproof is completed by applying H1.
Apply add_SNo_assoc with
minus_SNo x0,
x0,
x2,
λ x3 x4 . x4 = x2 leaving 4 subgoals.
The subproof is completed by applying L4.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply add_SNo_minus_SNo_linv with
x0,
λ x3 x4 . add_SNo x4 x2 = x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply add_SNo_0L with
x2.
The subproof is completed by applying H2.
Apply L5 with
λ x3 x4 . x3 = x2.
Apply H3 with
λ x3 x4 . add_SNo (minus_SNo x0) x4 = x2.
The subproof is completed by applying L6.