Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoLeE with
0,
x1,
SNoLe (mul_SNo x0 x1) 0 leaving 5 subgoals.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply mul_SNo_nonpos_pos with
x0,
x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H4: 0 = x1.
Apply H4 with
λ x2 x3 . SNoLe (mul_SNo x0 x2) 0.
Apply mul_SNo_zeroR with
x0,
λ x2 x3 . SNoLe x3 0 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNoLe_ref with 0.