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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: x1 = 0∀ x3 : ο . x3.
Assume H4: x0 = mul_SNo x1 x2.
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.