X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fnlibrary%2Flogic%2Fconnectives.ma;h=ea4642e90cce50dc45b1c488c7b58975d23deca6;hb=f8b4eb67c2437f7b5174d7dca46e102e0ac0d19d;hp=4d085995d4ea1a589af54e8552afdbe2fbf713e3;hpb=2c01ff6094173915e7023076ea48b5804dca7778;p=helm.git diff --git a/matita/matita/nlibrary/logic/connectives.ma b/matita/matita/nlibrary/logic/connectives.ma index 4d085995d..ea4642e90 100644 --- a/matita/matita/nlibrary/logic/connectives.ma +++ b/matita/matita/nlibrary/logic/connectives.ma @@ -14,43 +14,43 @@ include "logic/pts.ma". -ninductive True: CProp[0] ≝ +inductive True: CProp[0] ≝ I : True. -ninductive False: CProp[0] ≝. +inductive False: CProp[0] ≝. -ndefinition Not: CProp[0] → CProp[0] ≝ +definition Not: CProp[0] → CProp[0] ≝ λA. A → False. -interpretation "logical not" 'not x = (Not x). +interpretation "logical ot" 'not x = (Not x). -ninductive And (A,B:CProp[0]) : CProp[0] ≝ +inductive 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[0]) : CProp[0] ≝ +inductive 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[0]) (P:A → CProp[0]) : CProp[0] ≝ +inductive 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] ≝ +inductive 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). -ninductive sigma (A : Type[0]) (P : A → CProp[0]) : Type[0] ≝ +inductive 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] ≝ +record iff (A,B: CProp[0]) : CProp[0] ≝ { if: A → B; fi: B → A }.