Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι be given.
Assume H1: x3 ∈ x0.
Let x4 of type ι be given.
Assume H2: x4 ∈ x0.
Apply explicit_Nats_primrec_S with
x0,
x1,
x2,
x1,
λ x5 x6 . explicit_Nats_zero_plus x0 x1 x2 x4 x6,
x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.