X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fcprop_connectives.ma;h=c0bbdda18f3212715b49e5c8412cb7523c81e2ce;hb=42c44d828983e4ea2d115eba20a8020b62108384;hp=fe377cbd954d0fd9331935efc7360bdb380b12ba;hpb=0cc98ffd7308208cb26dae42435d1dcbd63b93fb;p=helm.git diff --git a/helm/software/matita/library/logic/cprop_connectives.ma b/helm/software/matita/library/logic/cprop_connectives.ma index fe377cbd9..c0bbdda18 100644 --- a/helm/software/matita/library/logic/cprop_connectives.ma +++ b/helm/software/matita/library/logic/cprop_connectives.ma @@ -12,6 +12,8 @@ (* *) (**************************************************************************) +include "logic/connectives.ma". + inductive Or (A,B:CProp) : CProp ≝ | Left : A → Or A B | Right : B → Or A B. @@ -56,6 +58,13 @@ notation < "hvbox(a break ∧ b break ∧ c break ∧ d)" with precedence 35 for interpretation "constructive quaternary and" 'and4 x y z t = (And4 x y z t). +record Iff (A,B:CProp) : CProp ≝ + { if: A → B; + fi: B → A + }. + +interpretation "logical iff" 'iff x y = (Iff x y). + inductive exT (A:Type) (P:A→CProp) : CProp ≝ ex_introT: ∀w:A. P w → exT A P. @@ -101,7 +110,6 @@ interpretation "exT2 \snd" 'pi2b x y = (pi2exT23 _ _ _ _ x y). inductive exT2 (A:Type) (P,Q:A→CProp) : CProp ≝ ex_introT2: ∀w:A. P w → Q w → exT2 A P Q. -alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)". definition Not : CProp → Prop ≝ λx:CProp.x → False. interpretation "constructive not" 'not x = (Not x).