Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H3: x1 = 0 ⟶ ∀ x3 : ο . x3.
Apply mul_SNo_nonzero_cancel with
x1,
div_SNo x0 x1,
x2 leaving 5 subgoals.
The subproof is completed by applying H1.
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.
The subproof is completed by applying H2.
Apply mul_div_SNo_invR with
x0,
x1,
λ x3 x4 . x4 = mul_SNo x1 x2 leaving 4 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 H4.