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cbf274c0
Commit
cbf274c0
authored
Nov 17, 2016
by
Robbert Krebbers
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Existentials commute with disjunction.
parent
4ecb139a
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base_logic/derived.v
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cbf274c0
...
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@@ -199,6 +199,13 @@ Lemma and_exist_r {A} P (Φ: A → uPred M) : (∃ a, Φ a) ∧ P ⊣⊢ ∃ a,
Proof
.
rewrite
-(
comm
_
P
)
and_exist_l
.
apply
exist_proper
=>
a
.
by
rewrite
comm
.
Qed
.
Lemma
or_exist
{
A
}
(
Φ
Ψ
:
A
→
uPred
M
)
:
(
∃
a
,
Φ
a
∨
Ψ
a
)
⊣
⊢
(
∃
a
,
Φ
a
)
∨
(
∃
a
,
Ψ
a
).
Proof
.
apply
(
anti_symm
(
⊢
)).
-
apply
exist_elim
=>
a
.
by
rewrite
-!(
exist_intro
a
).
-
apply
or_elim
;
apply
exist_elim
=>
a
;
rewrite
-(
exist_intro
a
)
;
auto
.
Qed
.
Lemma
pure_mono
φ
1
φ
2
:
(
φ
1
→
φ
2
)
→
■
φ
1
⊢
■
φ
2
.
Proof
.
intros
;
apply
pure_elim
with
φ
1
;
eauto
.
Qed
.
...
...
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