X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Flogic%2Fconnectives.ma;h=4d085995d4ea1a589af54e8552afdbe2fbf713e3;hb=1d7773584ddd6463b0941026f114b0173e3b6b72;hp=026e9216951c9224737b6493953317effd635369;hpb=1dd64d6c49db7dc0dc0ee39c30da4c7a043b8bde;p=helm.git diff --git a/helm/software/matita/nlibrary/logic/connectives.ma b/helm/software/matita/nlibrary/logic/connectives.ma index 026e92169..4d085995d 100644 --- a/helm/software/matita/nlibrary/logic/connectives.ma +++ b/helm/software/matita/nlibrary/logic/connectives.ma @@ -14,33 +14,43 @@ 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[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 ≝ +ninductive sigma (A : Type[0]) (P : A → CProp[0]) : Type[0] ≝ + sig_intro : ∀x:A.P x → sigma A P. + +interpretation "sigma" 'sigma \eta.p = (sigma ? p). + +nrecord iff (A,B: CProp[0]) : CProp[0] ≝ { if: A → B; fi: B → A }.