Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply mul_SNo_com with
x0,
x2,
λ x3 x4 . SNoLt x4 (mul_SNo x1 x2) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply mul_SNo_com with
x1,
x2,
λ x3 x4 . SNoLt (mul_SNo x2 x0) x4 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply pos_mul_SNo_Lt with
x2,
x0,
x1 leaving 5 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.