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Iris
stdpp
Commits
84fd0660
Commit
84fd0660
authored
May 30, 2019
by
Robbert Krebbers
Browse files
Add `set_fold_ind_L`.
parent
3bc16467
Pipeline
#17068
passed with stage
in 8 minutes and 27 seconds
Changes
1
Pipelines
1
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Inline
Side-by-side
theories/fin_sets.v
View file @
84fd0660
...
...
@@ -224,6 +224,11 @@ Proof.
rewrite
(
union_difference
{[
x
]}
X
)
by
set_solver
.
apply
Hadd
.
set_solver
.
apply
IH
.
set_solver
.
Qed
.
Lemma
set_fold_ind_L
`
{!
LeibnizEquiv
C
}
{
B
}
(
P
:
B
→
C
→
Prop
)
(
f
:
A
→
B
→
B
)
(
b
:
B
)
:
P
b
∅
→
(
∀
x
X
r
,
x
∉
X
→
P
r
X
→
P
(
f
x
r
)
({[
x
]}
∪
X
))
→
∀
X
,
P
(
set_fold
f
b
X
)
X
.
Proof
.
apply
set_fold_ind
.
by
intros
??
->
??
->%
leibniz_equiv
.
Qed
.
Lemma
set_fold_proper
{
B
}
(
R
:
relation
B
)
`
{!
Equivalence
R
}
(
f
:
A
→
B
→
B
)
(
b
:
B
)
`
{!
Proper
((=)
==>
R
==>
R
)
f
}
(
Hf
:
∀
a1
a2
b
,
R
(
f
a1
(
f
a2
b
))
(
f
a2
(
f
a1
b
)))
:
...
...
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