helm/software/matita/contribs/procedural/library/preamble.ma

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  13 (**************************************************************************)
  14
  15 (*
  16
  17 default "equality"
  18  cic:/Coq/Init/Logic/eq.ind
  19  cic:/Coq/Init/Logic/sym_eq.con
  20  cic:/Coq/Init/Logic/trans_eq.con
  21  cic:/Coq/Init/Logic/eq_ind.con
  22  cic:/Coq/Init/Logic/eq_ind_r.con
  23  cic:/Coq/Init/Logic/eq_rec.con
  24  cic:/Coq/Init/Logic/eq_rec_r.con
  25  cic:/Coq/Init/Logic/eq_rect.con
  26  cic:/Coq/Init/Logic/eq_rect_r.con
  27  cic:/Coq/Init/Logic/f_equal.con
  28  cic:/matita/procedural/Coq/preamble/f_equal1.con.
  29
  30 default "true"
  31  cic:/Coq/Init/Logic/True.ind.
  32 default "false"
  33  cic:/Coq/Init/Logic/False.ind.
  34 default "absurd"
  35  cic:/Coq/Init/Logic/absurd.con.
  36
  37 interpretation "Coq's leibnitz's equality" 'eq x y = (cic:/Coq/Init/Logic/eq.ind#xpointer(1/1) _ x y).
  38
  39 theorem f_equal1 : \forall A,B:Type.\forall f:A\to B.\forall x,y:A.
  40   x = y \to (f y) = (f x).
  41   intros.
  42   symmetry.
  43   apply cic:/Coq/Init/Logic/f_equal.con.
  44   assumption.
  45 qed.
  46
  47 alias id "land" = "cic:/matita/procedural/Coq/Init/Logic/and.ind#xpointer(1/1)".
  48
  49 *)