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5631e485
Commit
5631e485
authored
Oct 03, 2016
by
Robbert Krebbers
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Cancelation for union.
parent
d6875e7d
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prelude/collections.v
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5631e485
...
...
@@ -339,6 +339,11 @@ Section simple_collection.
Lemma
empty_union
X
Y
:
X
∪
Y
≡
∅
↔
X
≡
∅
∧
Y
≡
∅
.
Proof
.
set_solver
.
Qed
.
Lemma
union_cancel_l
X
Y
Z
:
Z
⊥
X
→
Z
⊥
Y
→
Z
∪
X
≡
Z
∪
Y
→
X
≡
Y
.
Proof
.
set_solver
.
Qed
.
Lemma
union_cancel_r
X
Y
Z
:
X
⊥
Z
→
Y
⊥
Z
→
X
∪
Z
≡
Y
∪
Z
→
X
≡
Y
.
Proof
.
set_solver
.
Qed
.
(** Empty *)
Lemma
elem_of_equiv_empty
X
:
X
≡
∅
↔
∀
x
,
x
∉
X
.
Proof
.
set_solver
.
Qed
.
...
...
@@ -455,6 +460,11 @@ Section simple_collection.
Lemma
empty_union_L
X
Y
:
X
∪
Y
=
∅
↔
X
=
∅
∧
Y
=
∅
.
Proof
.
unfold_leibniz
.
apply
empty_union
.
Qed
.
Lemma
union_cancel_l_L
X
Y
Z
:
Z
⊥
X
→
Z
⊥
Y
→
Z
∪
X
=
Z
∪
Y
→
X
=
Y
.
Proof
.
unfold_leibniz
.
apply
union_cancel_l
.
Qed
.
Lemma
union_cancel_r_L
X
Y
Z
:
X
⊥
Z
→
Y
⊥
Z
→
X
∪
Z
=
Y
∪
Z
→
X
=
Y
.
Proof
.
unfold_leibniz
.
apply
union_cancel_r
.
Qed
.
(** Empty *)
Lemma
elem_of_equiv_empty_L
X
:
X
=
∅
↔
∀
x
,
x
∉
X
.
Proof
.
unfold_leibniz
.
apply
elem_of_equiv_empty
.
Qed
.
...
...
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