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 mul_div_SNo_L with
x2,
x3,
div_SNo x0 x1,
λ x4 x5 . x5 = div_SNo (mul_SNo x0 x2) (mul_SNo x1 x3) leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply SNo_div_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply mul_div_SNo_R with
x0,
x1,
x2,
λ x4 x5 . div_SNo x5 x3 = div_SNo (mul_SNo x0 x2) (mul_SNo x1 x3) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply div_div_SNo with
mul_SNo x0 x2,
x1,
x3 leaving 3 subgoals.
Apply SNo_mul_SNo with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.