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David Swasey
coq-stdpp
Commits
64bedf4c
Commit
64bedf4c
authored
Aug 21, 2013
by
Robbert Krebbers
Browse files
Two basic De Morgan like laws for decidable propositions.
parent
1426e843
Changes
1
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Inline
Side-by-side
theories/decidable.v
View file @
64bedf4c
...
...
@@ -171,3 +171,9 @@ Instance uncurry_dec `(P_dec : ∀ (p : A * B), Decision (P p)) x y :
Instance
sig_eq_dec
`
(
P
:
A
→
Prop
)
`
{
∀
x
,
ProofIrrel
(
P
x
)}
`
{
∀
x
y
:
A
,
Decision
(
x
=
y
)}
(
x
y
:
sig
P
)
:
Decision
(
x
=
y
).
Proof
.
refine
(
cast_if
(
decide
(
`
x
=
`
y
)))
;
by
rewrite
sig_eq_pi
.
Defined
.
(** Some laws for decidable propositions *)
Lemma
not_and_l
{
P
Q
:
Prop
}
`
{
Decision
P
}
:
¬
(
P
∧
Q
)
↔
¬
P
∨
(
¬
Q
∧
P
).
Proof
.
destruct
(
decide
P
)
;
tauto
.
Qed
.
Lemma
not_and_r
{
P
Q
:
Prop
}
`
{
Decision
Q
}
:
¬
(
P
∧
Q
)
↔
(
¬
P
∧
Q
)
∨
¬
Q
.
Proof
.
destruct
(
decide
Q
)
;
tauto
.
Qed
.
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