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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: CSNo x0.
Assume H1: CSNo x1.
Assume H2: CSNo x2.
Assume H3: CSNo x3.
Assume H4: CSNo x4.
set y5 to be add_CSNo x3 (add_CSNo x4 (add_CSNo x0 (add_CSNo x1 x2)))
Claim L5: ∀ x6 : ι → ο . x6 y5 ⟶ x6 (add_CSNo x0 (add_CSNo x1 (add_CSNo x2 (add_CSNo x3 x4))))
Let x6 of type ι → ο be given.
Assume H5: x6 (add_CSNo x4 (add_CSNo y5 (add_CSNo x1 (add_CSNo x2 x3)))).
Apply unknownprop_bb314311587f05f6fc68994eed567dad930d3a512d178f2cfd47dd38479aaffc 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_bb314311587f05f6fc68994eed567dad930d3a512d178f2cfd47dd38479aaffc 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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