X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Flogic%2Fconnectives.ma;h=34661dc8015e62a19403fb16e337359acb59c19e;hb=8cb2490b5b202549a596cfd1d0f166a5ee43fc4e;hp=a149bc9ddf4e88133871e0d73aed62fe02fb613b;hpb=12bebae6f57b3a671a1aa29662d5ed7208a85667;p=helm.git diff --git a/helm/software/matita/nlibrary/logic/connectives.ma b/helm/software/matita/nlibrary/logic/connectives.ma index a149bc9dd..34661dc80 100644 --- a/helm/software/matita/nlibrary/logic/connectives.ma +++ b/helm/software/matita/nlibrary/logic/connectives.ma @@ -14,38 +14,38 @@ include "logic/pts.ma". -ninductive True: CProp ≝ +ninductive True: CProp[0] ≝ I : True. -ninductive False: CProp ≝. +ninductive False: CProp[0] ≝. -ndefinition Not: CProp → CProp ≝ +ndefinition Not: CProp[0] → CProp[0] ≝ λA. A → False. interpretation "logical not" 'not x = (Not x). -ninductive And (A,B:CProp) : CProp ≝ +ninductive And (A,B:CProp[0]) : CProp[0] ≝ conj : A → B → And A B. interpretation "logical and" 'and x y = (And x y). -ninductive Or (A,B:CProp) : CProp ≝ +ninductive Or (A,B:CProp[0]) : CProp[0] ≝ or_introl : A → Or A B | or_intror : B → Or A B. interpretation "logical or" 'or x y = (Or x y). -ninductive Ex (A:Type) (P:A → CProp) : CProp ≝ +ninductive Ex (A:Type[0]) (P:A → CProp[0]) : CProp[0] ≝ ex_intro: ∀x:A. P x → Ex A P. -ninductive Ex1 (A:Type[1]) (P:A → CProp) : CProp[1] ≝ +ninductive Ex1 (A:Type[1]) (P:A → CProp[0]) : 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 ≝ +nrecord iff (A,B: CProp[0]) : CProp[0] ≝ { if: A → B; fi: B → A }.