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Proofgold Proof
pf
Apply add_nat_SR with
u5
,
u6
,
λ x0 x1 .
x1
=
u12
leaving 2 subgoals.
The subproof is completed by applying nat_6.
set y0 to be
ordsucc
(
add_nat
u5
u6
)
set y1 to be
ordsucc
u11
Claim L0:
∀ x2 :
ι → ο
.
x2
y1
⟶
x2
y0
Let x2 of type
ι
→
ο
be given.
Assume H0:
x2
(
ordsucc
u11
)
.
set y3 to be
λ x3 .
x2
Apply unknownprop_0b9ffec33b58796014d5e2e27ec991760d5cb69fe8e4add65e322eaea4c8c56c 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.
■