Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply SNoLtLe_or with
x1,
x2,
SNoLt x1 x2 leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
Apply FalseE with
SNoLt x1 x2.
Apply SNoLt_irref with
mul_SNo x0 x2.
Apply SNoLeLt_tra with
mul_SNo x0 x2,
mul_SNo x0 x1,
mul_SNo x0 x2 leaving 5 subgoals.
Apply SNo_mul_SNo with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply SNo_mul_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply SNo_mul_SNo with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply nonneg_mul_SNo_Le with
x0,
x2,
x1 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H2.
The subproof is completed by applying H5.
The subproof is completed by applying H4.