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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.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNo x4.
Apply mul_SNo_rotate_4_1 with x1, x2, x3, x4, λ x5 x6 . mul_SNo x0 x6 = mul_SNo x4 (mul_SNo x0 (mul_SNo x1 (mul_SNo x2 x3))) leaving 5 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply mul_SNo_com_3_0_1 with x0, x4, mul_SNo x1 (mul_SNo x2 x3) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
Apply SNo_mul_SNo_3 with x1, x2, x3 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.