Library Coq.Logic.Classical_Pred_Type
Classical Predicate Logic on Type
de Morgan laws for quantifiers
Lemma not_all_not_ex :
forall P:
U -> Prop,
~ (forall n:
U,
~ P n) -> exists n :
U, P n.
Lemma not_all_ex_not :
forall P:
U -> Prop,
~ (forall n:
U,
P n) -> exists n :
U, ~ P n.
Lemma not_ex_all_not :
forall P:
U -> Prop,
~ (exists n :
U, P n) -> forall n:
U,
~ P n.
Lemma not_ex_not_all :
forall P:
U -> Prop,
~ (exists n :
U, ~ P n) -> forall n:
U,
P n.
Lemma ex_not_not_all :
forall P:
U -> Prop,
(exists n :
U, ~ P n) -> ~ (forall n:
U,
P n).
Lemma all_not_not_ex :
forall P:
U -> Prop,
(forall n:
U,
~ P n) -> ~ (exists n :
U, P n).
End Generic.