helm/matita/tests/rewrite.ma

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  14
  15 set "baseuri" "cic:/matita/tests/rewrite/".
  16 include "coq.ma".
  17
  18 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
  19 alias num (instance 0) = "natural number".
  20 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  21 alias symbol "plus" (instance 0) = "Coq's natural plus".
  22 alias id "plus_n_O" = "cic:/Coq/Init/Peano/plus_n_O.con".
  23
  24 theorem a:
  25   \forall a,b:nat.
  26   a = b \to b + a + b + a= (\lambda j.((\lambda w.((\lambda x.x + b + w + j) a)) b)) a.
  27 intros.
  28 rewrite < H in \vdash (? ? ? ((\lambda j.((\lambda w.%) ?)) ?)).
  29
  30 rewrite < H in \vdash (? ? % ?).
  31
  32 simplify in \vdash (? ? ? ((\lambda _.((\lambda _.%) ?)) ?)).
  33
  34 rewrite < H in \vdash (? ? ? (% ?)).
  35 simplify.
  36 reflexivity.
  37 qed.
  38
  39 theorem t: \forall n. 0=0 \to n = n + 0.
  40  intros.
  41  apply plus_n_O.
  42 qed.
  43
  44 (* In this test "rewrite < t" should open a new goal 0=0 and put it in *)
  45 (* the goallist so that the THEN tactical closes it using reflexivity. *)
  46 theorem foo: \forall n. n = n + 0.
  47  intros.
  48  rewrite < t; reflexivity.
  49 qed.