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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Assume H0:
nat_p
x1
.
Assume H1:
ordsucc
(
96eca..
x0
x1
)
∈
x0
.
Apply nat_primrec_S with
0
,
λ x2 x3 .
If_i
(
ordsucc
x3
∈
x0
)
(
ordsucc
x3
)
0
,
x1
,
λ x2 x3 .
x3
=
ordsucc
(
96eca..
x0
x1
)
leaving 2 subgoals.
The subproof is completed by applying H0.
Apply If_i_1 with
ordsucc
(
96eca..
x0
x1
)
∈
x0
,
ordsucc
(
96eca..
x0
x1
)
,
0
.
The subproof is completed by applying H1.
■