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

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