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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Assume H0:
80242..
x0
.
Assume H1:
80242..
x1
.
Assume H2:
099f3..
x0
x1
.
Apply unknownprop_9155775841857cb348ae79731186aa077c95466dd39af675bcbf421e2bc4c9da with
x0
,
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x0
)
leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H3:
and
(
and
(
80242..
(
f4dc0..
x0
)
)
(
∀ x2 .
prim1
x2
(
23e07..
x0
)
⟶
099f3..
(
f4dc0..
x0
)
(
f4dc0..
x2
)
)
)
(
∀ x2 .
prim1
x2
(
5246e..
x0
)
⟶
099f3..
(
f4dc0..
x2
)
(
f4dc0..
x0
)
)
.
Apply H3 with
02b90..
(
94f9e..
(
5246e..
x0
)
f4dc0..
)
(
94f9e..
(
23e07..
x0
)
f4dc0..
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x0
)
.
Assume H4:
and
(
80242..
(
f4dc0..
x0
)
)
(
∀ x2 .
prim1
x2
(
23e07..
x0
)
⟶
099f3..
(
f4dc0..
x0
)
(
f4dc0..
x2
)
)
.
Apply H4 with
(
∀ x2 .
prim1
x2
(
5246e..
x0
)
⟶
099f3..
(
f4dc0..
x2
)
(
f4dc0..
x0
)
)
⟶
02b90..
(
94f9e..
(
5246e..
x0
)
f4dc0..
)
(
94f9e..
(
23e07..
x0
)
f4dc0..
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x0
)
.
Assume H5:
80242..
(
f4dc0..
x0
)
.
Assume H6:
∀ x2 .
prim1
x2
(
23e07..
x0
)
⟶
099f3..
(
f4dc0..
x0
)
(
f4dc0..
x2
)
.
Assume H7:
∀ x2 .
prim1
x2
(
5246e..
x0
)
⟶
099f3..
(
f4dc0..
x2
)
(
f4dc0..
x0
)
.
Assume H8:
02b90..
(
94f9e..
(
5246e..
x0
)
f4dc0..
)
(
94f9e..
(
23e07..
x0
)
f4dc0..
)
.
Apply unknownprop_9155775841857cb348ae79731186aa077c95466dd39af675bcbf421e2bc4c9da with
x1
,
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x0
)
leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H9:
and
(
and
(
80242..
(
f4dc0..
x1
)
)
(
∀ x2 .
prim1
x2
(
23e07..
x1
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x2
)
)
)
(
∀ x2 .
prim1
x2
(
5246e..
x1
)
⟶
099f3..
(
f4dc0..
x2
)
(
f4dc0..
x1
)
)
.
Apply H9 with
02b90..
(
94f9e..
(
5246e..
x1
)
f4dc0..
)
(
94f9e..
(
23e07..
x1
)
f4dc0..
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x0
)
.
Assume H10:
and
(
80242..
(
f4dc0..
x1
)
)
(
∀ x2 .
prim1
x2
(
23e07..
x1
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x2
)
)
.
Apply H10 with
(
∀ x2 .
prim1
x2
(
5246e..
x1
)
⟶
099f3..
(
f4dc0..
x2
)
(
f4dc0..
x1
)
)
⟶
02b90..
(
94f9e..
(
5246e..
x1
)
f4dc0..
)
(
94f9e..
(
23e07..
x1
)
f4dc0..
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x0
)
.
Assume H11:
80242..
(
f4dc0..
x1
)
.
Assume H12:
∀ x2 .
prim1
x2
(
23e07..
x1
)
⟶
099f3..
(
f4dc0..
x1
)
(
f4dc0..
x2
)
.
Assume H13:
∀ x2 .
prim1
x2
(
5246e..
x1
)
⟶
099f3..
(
f4dc0..
x2
)
(
f4dc0..
x1
)
.
Assume H14:
02b90..
(
94f9e..
(
5246e..
x1
)
f4dc0..
)
(
94f9e..
(
23e07..
x1
)
f4dc0..
)
.
Apply unknownprop_334a5a4dfd5441f12538cd3c70458238b05308c372afbd4cf94b09dd8e7afe85 with
x0
,
x1
,
099f3..
(
f4dc0..
x1
)
...
leaving 6 subgoals.
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