X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Flogic%2Fconnectives.ma;h=a149bc9ddf4e88133871e0d73aed62fe02fb613b;hb=12bebae6f57b3a671a1aa29662d5ed7208a85667;hp=6eb2375dcc895b3b8e4e6068572345382f349e34;hpb=a17430d258e886b5164fca3d65ee7da7c40e6a36;p=helm.git diff --git a/helm/software/matita/nlibrary/logic/connectives.ma b/helm/software/matita/nlibrary/logic/connectives.ma index 6eb2375dc..a149bc9dd 100644 --- a/helm/software/matita/nlibrary/logic/connectives.ma +++ b/helm/software/matita/nlibrary/logic/connectives.ma @@ -18,9 +18,6 @@ ninductive True: CProp ≝ I : True. ninductive False: CProp ≝. -(* elimination principle *) -ndefinition False_rect ≝ λP: False → Type.λp: False. - match p in False return λp. P p with []. ndefinition Not: CProp → CProp ≝ λA. A → False. @@ -41,4 +38,24 @@ interpretation "logical or" 'or x y = (Or x y). ninductive Ex (A:Type) (P:A → CProp) : CProp ≝ ex_intro: ∀x:A. P x → Ex A P. + +ninductive Ex1 (A:Type[1]) (P:A → CProp) : CProp[1] ≝ + ex_intro1: ∀x:A. P x → Ex1 A P. + +interpretation "exists1" 'exists x = (Ex1 ? x). interpretation "exists" 'exists x = (Ex ? x). + +nrecord iff (A,B: CProp) : CProp ≝ + { if: A → B; + fi: B → A + }. + +notation > "hvbox(a break \liff b)" + left associative with precedence 25 +for @{ 'iff $a $b }. + +notation "hvbox(a break \leftrightarrow b)" + left associative with precedence 25 +for @{ 'iff $a $b }. + +interpretation "logical iff" 'iff x y = (iff x y).