Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply SNo_add_SNo_3c with
mul_SNo x2 x1,
mul_SNo x0 x3,
mul_SNo x2 x3 leaving 3 subgoals.
Apply SNo_mul_SNo with
x2,
x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
Apply SNo_mul_SNo with
x0,
x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply SNo_mul_SNo with
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.