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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
80242..
x0
.
Claim L1:
...
...
Claim L2:
...
...
Apply unknownprop_e277188ae242e07bd6727f267e38747aecd739d129890076e65b92339f7beb98 with
23e07..
x0
,
5246e..
x0
,
x0
=
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
leaving 2 subgoals.
The subproof is completed by applying L2.
Assume H3:
and
(
and
(
and
(
80242..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
prim1
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
4ae4a..
(
0ac37..
(
a842e..
(
23e07..
x0
)
(
λ x1 .
4ae4a..
(
e4431..
x1
)
)
)
(
a842e..
(
5246e..
x0
)
(
λ x1 .
4ae4a..
(
e4431..
x1
)
)
)
)
)
)
)
(
∀ x1 .
prim1
x1
(
23e07..
x0
)
⟶
099f3..
x1
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
)
(
∀ x1 .
prim1
x1
(
5246e..
x0
)
⟶
099f3..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
x1
)
.
Apply H3 with
(
∀ x1 .
80242..
x1
⟶
(
∀ x2 .
prim1
x2
(
23e07..
x0
)
⟶
099f3..
x2
x1
)
⟶
(
∀ x2 .
prim1
x2
(
5246e..
x0
)
⟶
099f3..
x1
x2
)
⟶
and
(
Subq
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
e4431..
x1
)
)
(
SNoEq_
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
x1
)
)
⟶
x0
=
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
.
Assume H4:
and
(
and
(
80242..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
prim1
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
4ae4a..
(
0ac37..
(
a842e..
(
23e07..
x0
)
(
λ x1 .
4ae4a..
(
e4431..
x1
)
)
)
(
a842e..
(
5246e..
x0
)
(
λ x1 .
4ae4a..
(
e4431..
x1
)
)
)
)
)
)
)
(
∀ x1 .
prim1
x1
(
23e07..
x0
)
⟶
099f3..
x1
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
.
Apply H4 with
(
∀ x1 .
prim1
x1
(
5246e..
x0
)
⟶
099f3..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
x1
)
⟶
(
∀ x1 .
80242..
x1
⟶
(
∀ x2 .
prim1
x2
(
23e07..
x0
)
⟶
099f3..
x2
x1
)
⟶
(
∀ x2 .
prim1
x2
(
5246e..
x0
)
⟶
099f3..
x1
x2
)
⟶
and
(
Subq
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
e4431..
x1
)
)
(
SNoEq_
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
x1
)
)
⟶
x0
=
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
.
Assume H5:
and
(
80242..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
prim1
(
e4431..
(
02a50..
(
23e07..
x0
)
(
5246e..
x0
)
)
)
(
4ae4a..
(
0ac37..
(
a842e..
(
23e07..
x0
)
(
λ x1 .
4ae4a..
(
e4431..
x1
)
)
)
(
a842e..
(
5246e..
x0
)
(
λ x1 .
4ae4a..
...
)
)
)
)
)
.
...
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