Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoLtLe_or with
x0,
0,
SNoLe 0 (mul_SNo x0 x1) 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 x1.
Apply mul_SNo_neg_neg with
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
Apply SNoLe_antisym with
x0,
0,
λ x2 x3 . SNoLe 0 (mul_SNo x3 x1) leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply mul_SNo_zeroL with
x1,
λ x2 x3 . SNoLe 0 x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying SNoLe_ref with 0.