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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.
set y5 to be mul_SNo x3 (mul_SNo x4 (mul_SNo x0 (mul_SNo x1 x2)))
Claim L5: ∀ x6 : ι → ο . x6 y5 ⟶ x6 (mul_SNo x0 (mul_SNo x1 (mul_SNo x2 (mul_SNo x3 x4))))
Let x6 of type ι → ο be given.
Assume H5: x6 (mul_SNo x4 (mul_SNo y5 (mul_SNo x1 (mul_SNo x2 x3)))).
Apply unknownprop_305c941cfd7ab4beb34887f93a32ac1eea31589c106996d6116b806592159515 with x1, x2, x3, x4, y5, λ x7 . x6 leaving 6 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 H3.
The subproof is completed by applying H4.
Apply unknownprop_305c941cfd7ab4beb34887f93a32ac1eea31589c106996d6116b806592159515 with y5, x1, x2, x3, x4, λ x7 . x6 leaving 6 subgoals.
The subproof is completed by applying H4.
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 H3.
The subproof is completed by applying H5.
Let x6 of type ι → ι → ο be given.
Apply L5 with λ x7 . x6 x7 y5 ⟶ x6 y5 x7.
Assume H6: x6 y5 y5.
The subproof is completed by applying H6.
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