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George Pirlea
Iris
Commits
7a7e1d22
Commit
7a7e1d22
authored
May 17, 2018
by
Robbert Krebbers
Browse files
Prove `□ False ⊣⊢ False`.
parent
0aeb4cdc
Changes
1
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Inline
Side-by-side
theories/bi/derived_laws_bi.v
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7a7e1d22
...
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@@ -988,6 +988,8 @@ Proof.
by
rewrite
/
bi_intuitionistically
-
persistently_True_emp
persistently_pure
affinely_True_emp
affinely_emp
.
Qed
.
Lemma
intuitionistically_False
:
□
False
⊣
⊢
False
.
Proof
.
by
rewrite
/
bi_intuitionistically
persistently_pure
affinely_False
.
Qed
.
Lemma
intuitionistically_True_emp
:
□
True
⊣
⊢
emp
.
Proof
.
rewrite
-
intuitionistically_emp
/
bi_intuitionistically
...
...
@@ -1179,6 +1181,8 @@ Proof. destruct p; simpl; auto using intuitionistically_intro'. Qed.
Lemma
intuitionistically_if_emp
p
:
□
?p
emp
⊣
⊢
emp
.
Proof
.
destruct
p
;
simpl
;
auto
using
intuitionistically_emp
.
Qed
.
Lemma
intuitionistically_if_False
p
:
□
?p
False
⊣
⊢
False
.
Proof
.
destruct
p
;
simpl
;
auto
using
intuitionistically_False
.
Qed
.
Lemma
intuitionistically_if_and
p
P
Q
:
□
?p
(
P
∧
Q
)
⊣
⊢
□
?p
P
∧
□
?p
Q
.
Proof
.
destruct
p
;
simpl
;
auto
using
intuitionistically_and
.
Qed
.
Lemma
intuitionistically_if_or
p
P
Q
:
□
?p
(
P
∨
Q
)
⊣
⊢
□
?p
P
∨
□
?p
Q
.
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