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.
Apply explicit_Nats_primrec_base with
x0,
x1,
x2,
x1,
λ x4 x5 . explicit_Nats_zero_plus x0 x1 x2 x3 x5.
The subproof is completed by applying H0.