Let x0 of type ι be given.
Apply SNoLtLe_or with
x0,
0,
SNoLe 0 (mul_SNo x0 x0) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
Apply SNoLtLe with
0,
mul_SNo x0 x0.
Apply mul_SNo_zeroR with
x0,
λ x1 x2 . SNoLt x1 (mul_SNo x0 x0) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply neg_mul_SNo_Lt with
x0,
0,
x0 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply mul_SNo_zeroR with
x0,
λ x1 x2 . SNoLe x1 (mul_SNo x0 x0) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply nonneg_mul_SNo_Le with
x0,
0,
x0 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.