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Proofgold Proof
pf
Apply add_nat_SR with
u31
,
20
,
λ x0 x1 .
x1
=
u52
leaving 2 subgoals.
The subproof is completed by applying unknownprop_07ad204b3b4fc2b51cd8392b0e6a88916124d7f0f3dbf696bec5a683b0ea9dae.
set y0 to be
ordsucc
(
add_nat
u31
u20
)
set y1 to be
ordsucc
u51
Claim L0:
∀ x2 :
ι → ο
.
x2
y1
⟶
x2
y0
Let x2 of type
ι
→
ο
be given.
Assume H0:
x2
(
ordsucc
u51
)
.
set y3 to be
λ x3 .
x2
Apply unknownprop_ded474503863d61ff8d88743109f0c88dc78796c830234726d6e6fd3c83d5ece 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.
■