matita/contribs/LAMBDA-TYPES/Level-1/Preamble.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/Preamble".
  16
  17 include "legacy/coq.ma".
  18
  19 (* FG/CSC: These aliases should disappear: we would like to write something
  20  *         like: "disambiguate in cic:/Coq/*"
  21  *)
  22 alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
  23 alias id "or" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1)".
  24 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
  25 alias id "eq" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1)".
  26 alias id "plus" = "cic:/Coq/Init/Peano/plus.con".
  27 alias id "le_trans" = "cic:/Coq/Arith/Le/le_trans.con".
  28 alias id "le_plus_r" = "cic:/Coq/Arith/Plus/le_plus_r.con".
  29 alias id "le" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1)".
  30 alias id "ex" = "cic:/Coq/Init/Logic/ex.ind#xpointer(1/1)".
  31 alias id "ex2" = "cic:/Coq/Init/Logic/ex2.ind#xpointer(1/1)".
  32 alias id "true" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1/1)".
  33 alias id "false" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1/2)".
  34 alias id "bool" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1)".
  35 alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
  36 alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
  37 alias id "eq_ind" = "cic:/Coq/Init/Logic/eq_ind.con".
  38 alias id "or_introl" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1/1)".
  39 alias id "or_intror" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1/2)".
  40 alias id "False_ind" = "cic:/Coq/Init/Logic/False_ind.con".
  41 alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
  42 alias id "I" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1/1)".
  43 alias id "minus" = "cic:/Coq/Init/Peano/minus.con".
  44
  45 theorem f_equal: \forall A,B:Type. \forall f:A \to B.
  46                  \forall x,y:A. x = y \to f x = f y.
  47  intros. elim H. reflexivity.
  48 qed.
  49
  50 theorem sym_eq: \forall A:Type. \forall x,y:A. x = y \to y = x.
  51  intros. rewrite > H. reflexivity.
  52 qed.
  53
  54 theorem sym_not_eq: \forall A:Type. \forall x,y:A. x \neq y \to y \neq x.
  55  unfold not. intros. apply H. symmetry. assumption.
  56 qed.