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.

Assume H0: CSNo x1.

Assume H1: CSNo x2.

Assume H2: CSNo x3.

set y4 to be add_CSNo x0 (add_CSNo x2 (add_CSNo x1 x3))

Claim L3: ∀ x5 : ι → ο . x5 y4 ⟶ x5 (add_CSNo x0 (add_CSNo x1 (add_CSNo x2 x3)))

Let x5 of type ι → ο be given.

Apply unknownprop_da96b87d1828fc8ba863b6e04bdabe0039a91c2aa965c2060e150e0d03b88cbb with x2, x3, y4, λ x6 x7 . (λ x8 . x5) (add_CSNo x1 x6) (add_CSNo x1 x7) leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

The subproof is completed by applying H2.

Let x5 of type ι → ι → ο be given.

Apply L3 with λ x6 . x5 x6 y4 ⟶ x5 y4 x6.

Assume H4: x5 y4 y4.

The subproof is completed by applying H4.

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Proofgold Proof