Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H2: x1 = 0 ⟶ ∀ x2 : ο . x2.
Apply mul_SNo_assoc with
x0,
recip_SNo x1,
x1,
λ x2 x3 . x2 = x0 leaving 4 subgoals.
The subproof is completed by applying H0.
Apply SNo_recip_SNo with
x1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
Apply recip_SNo_invL with
x1,
λ x2 x3 . mul_SNo x0 x3 = x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply mul_SNo_oneR with
x0.
The subproof is completed by applying H0.