Library Coq.Logic.Classical_Pred_Set
This file is obsolete, use Classical_Pred_Type.v via Classical.v
instead
Classical Predicate Logic on Set
de Morgan laws for quantifiers
Lemma not_all_ex_not :
forall P:
U ->
Prop,
~ (forall n:
U,
P n) ->
exists n : U, ~ P n.
Lemma not_all_not_ex :
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.