Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι be given.

Assume H0: explicit_Nats x0 x1 x2.

Let x3 of type ι be given.

Assume H1: prim1 x3 x0.

Let x4 of type ι be given.

Assume H2: prim1 x4 x0.

Apply explicit_Nats_primrec_S with x0, x1, x2, x4, λ x5 x6 . explicit_Nats_one_plus x0 x1 x2 x4 x6, x3 leaving 2 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

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Proofgold Proof