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Proofgold Proof
pf
Apply add_nat_SR with
u31
,
9
,
λ x0 x1 .
x1
=
u41
leaving 2 subgoals.
The subproof is completed by applying nat_9.
set y0 to be
ordsucc
(
add_nat
u31
u9
)
set y1 to be
ordsucc
u40
Claim L0:
∀ x2 :
ι → ο
.
x2
y1
⟶
x2
y0
Let x2 of type
ι
→
ο
be given.
Assume H0:
x2
(
ordsucc
u40
)
.
set y3 to be
λ x3 .
x2
Apply unknownprop_40321bc2a3d6e40b1c8e9b6e2bcb404f46d0fb163eca5ca029462b991ec2fcae with
λ x4 x5 .
y3
(
ordsucc
x4
)
(
ordsucc
x5
)
.
The subproof is completed by applying H0.
Let x2 of type
ι
→
ι
→
ο
be given.
Apply L0 with
λ x3 .
x2
x3
y1
⟶
x2
y1
x3
.
Assume H1:
x2
y1
y1
.
The subproof is completed by applying H1.
■