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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
→
ι
be given.
The subproof is completed by applying nat_primrec_S with
lam
2
(
λ x2 .
If_i
(
x2
=
0
)
(
Sing
0
)
0
)
,
λ x2 x3 .
lam
2
(
λ x4 .
If_i
(
x4
=
0
)
(
binunion
(
binunion
(
ap
x3
0
)
(
SNo_recipauxset
(
ap
x3
0
)
x0
(
SNoR
x0
)
x1
)
)
(
SNo_recipauxset
(
ap
x3
1
)
x0
(
SNoL_pos
x0
)
x1
)
)
(
binunion
(
binunion
(
ap
x3
1
)
(
SNo_recipauxset
(
ap
x3
0
)
x0
(
SNoL_pos
x0
)
x1
)
)
(
SNo_recipauxset
(
ap
x3
1
)
x0
(
SNoR
x0
)
x1
)
)
)
.
■