Claim L0: ∀ x0 x1 x2 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ add_SNo (add_SNo x0 x1) x2 = add_SNo x0 (add_SNo x1 x2)

Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Assume H0: SNo x0.

Assume H1: SNo x1.

Assume H2: SNo x2.

Let x3 of type ι → ι → ο be given.

Apply add_SNo_assoc with x0, x1, x2, λ x4 x5 . x3 x5 x4 leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

The subproof is completed by applying H2.

Apply CD_add_assoc with Sing 2, SNo, add_SNo leaving 3 subgoals.

The subproof is completed by applying complex_tag_fresh.

The subproof is completed by applying SNo_add_SNo.

The subproof is completed by applying L0.

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Proofgold Proof