Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply mul_SNo_oneR with
x2,
λ x3 x4 . mul_SNo x0 (mul_SNo x1 x3) = mul_SNo x1 (mul_SNo x2 x0) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply mul_SNo_oneR with
x0,
λ x3 x4 . mul_SNo x0 (mul_SNo x1 (mul_SNo x2 1)) = mul_SNo x1 (mul_SNo x2 x3) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_f4ba9e731338e2516399335fafd38bd49a40052babab3a48375eefd54d83a9ae with
x0,
x1,
x2,
1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying SNo_1.