Expérimentation de NewDestruct et parfois NewInduction

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1880 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 29 insertions, 29 deletions

diff --git a/theories/Arith/Between.v b/theories/Arith/Between.v
index ab22eca22..e6b444601 100755
--- a/theories/Arith/Between.v
+++ b/theories/Arith/Between.v
@@ -22,29 +22,29 @@ Hint constr_between : arith v62 := Constructors between.
 
 Lemma bet_eq : (k,l:nat)(l=k)->(between k l).
 Proof.
-Induction 1; Auto with arith.
+NewInduction 1; Auto with arith.
 Qed.
 
 Hints Resolve bet_eq : arith v62.
 
 Lemma between_le : (k,l:nat)(between k l)->(le k l).
 Proof.
-Induction 1; Auto with arith.
+NewInduction 1; Auto with arith.
 Qed.
 Hints Immediate between_le : arith v62.
 
 Lemma between_Sk_l : (k,l:nat)(between k l)->(le (S k) l)->(between (S k) l).
 Proof.
-Induction 1.
+NewInduction 1.
 Intros; Absurd (le (S k) k); Auto with arith.
-Induction 1; Auto with arith.
+Induction H; Auto with arith.
 Qed.
 Hints Resolve between_Sk_l : arith v62.
 
 Lemma between_restr : 
   (k,l,m:nat)(le k l)->(le l m)->(between k m)->(between l m).
 Proof.
-Induction 1; Auto with arith.
+NewInduction 1; Auto with arith.
 Qed.
 
 Inductive exists [k:nat] : nat -> Prop
@@ -55,7 +55,7 @@ Hint constr_exists : arith v62 := Constructors exists.
 
 Lemma exists_le_S : (k,l:nat)(exists k l)->(le (S k) l).
 Proof.
-Induction 1; Auto with arith.
+NewInduction 1; Auto with arith.
 Qed.
 
 Lemma exists_lt : (k,l:nat)(exists k l)->(lt k l).
@@ -78,55 +78,55 @@ Hints Resolve in_int_intro : arith v62.
 
 Lemma in_int_lt : (p,q,r:nat)(in_int p q r)->(lt p q).
 Proof.
-Induction 1; Intros.
+NewInduction 1; Intros.
 Apply le_lt_trans with r; Auto with arith.
 Qed.
 
 Lemma in_int_p_Sq : 
   (p,q,r:nat)(in_int p (S q) r)->((in_int p q r) \/ <nat>r=q).
 Proof.
-Induction 1; Intros.
+NewInduction 1; Intros.
 Elim (le_lt_or_eq r q); Auto with arith.
 Qed.
 
 Lemma in_int_S : (p,q,r:nat)(in_int p q r)->(in_int p (S q) r).
 Proof.
-Induction 1;Auto with arith.
+NewInduction 1;Auto with arith.
 Qed.
 Hints Resolve in_int_S : arith v62.
 
 Lemma in_int_Sp_q : (p,q,r:nat)(in_int (S p) q r)->(in_int p q r).
 Proof.
-Induction 1; Auto with arith.
+NewInduction 1; Auto with arith.
 Qed.
 Hints Immediate in_int_Sp_q : arith v62.
 
 Lemma between_in_int : (k,l:nat)(between k l)->(r:nat)(in_int k l r)->(P r).
 Proof.
-Induction 1; Intros.
+NewInduction 1; Intros.
 Absurd (lt k k); Auto with arith.
 Apply in_int_lt with r; Auto with arith.
-Elim (in_int_p_Sq k l0 r); Intros; Auto with arith.
-Rewrite H4; Trivial with arith.
+Elim (in_int_p_Sq k l r); Intros; Auto with arith.
+Rewrite H2; Trivial with arith.
 Qed.
 
 Lemma in_int_between : 
   (k,l:nat)(le k l)->((r:nat)(in_int k l r)->(P r))->(between k l).
 Proof.
-Induction 1; Auto with arith.
+NewInduction 1; Auto with arith.
 Qed.
 
 Lemma exists_in_int : 
   (k,l:nat)(exists k l)->(EX m:nat | (in_int k l m) & (Q m)).
 Proof.
-Induction 1.
-Induction 2; Intros p inp Qp; Exists p; Auto with arith.
-Intros; Exists l0; Auto with arith.
+NewInduction 1.
+Case IHexists; Intros p inp Qp; Exists p; Auto with arith.
+Exists l; Auto with arith.
 Qed.
 
 Lemma in_int_exists : (k,l,r:nat)(in_int k l r)->(Q r)->(exists k l).
 Proof.
-Induction 1; Intros.
+NewInduction 1; Intros.
 Elim H1; Auto with arith.
 Qed.
 
@@ -134,23 +134,23 @@ Lemma between_or_exists :
   (k,l:nat)(le k l)->((n:nat)(in_int k l n)->((P n)\/(Q n)))
      ->((between k l)\/(exists k l)).
 Proof.
-Induction 1; Intros; Auto with arith.
-Elim H1; Intro; Auto with arith.
-Elim (H2 m); Auto with arith.
+NewInduction 1; Intros; Auto with arith.
+Elim IHle; Intro; Auto with arith.
+Elim (H0 m); Auto with arith.
 Qed.
 
 Lemma between_not_exists : (k,l:nat)(between k l)->
      ((n:nat)(in_int k l n) -> (P n) -> ~(Q n))
      -> ~(exists k l).
 Proof.
-Induction 1; Red; Intros.
+NewInduction 1; Red; Intros.
 Absurd (lt k k); Auto with arith.
-Absurd (Q l0); Auto with arith.
-Elim (exists_in_int k (S l0)); Auto with arith; Intros l' inl' Ql'.
-Replace l0 with l'; Auto with arith.
+Absurd (Q l); Auto with arith.
+Elim (exists_in_int k (S l)); Auto with arith; Intros l' inl' Ql'.
+Replace l with l'; Auto with arith.
 Elim inl'; Intros.
-Elim (le_lt_or_eq l' l0); Auto with arith; Intros.
-Absurd (exists k l0); Auto with arith.
+Elim (le_lt_or_eq l' l); Auto with arith; Intros.
+Absurd (exists k l); Auto with arith.
 Apply in_int_exists with l'; Auto with arith.
 Qed.
 
@@ -161,7 +161,7 @@ Inductive nth [init:nat] : nat->nat->Prop
 
 Lemma nth_le : (init,l,n:nat)(nth init l n)->(le init l).
 Proof.
-Induction 1; Intros; Auto with arith.
+NewInduction 1; Intros; Auto with arith.
 Apply le_trans with (S k); Auto with arith.
 Qed.
 
@@ -169,7 +169,7 @@ Definition eventually := [n:nat](EX k:nat | (le k n) & (Q k)).
 
 Lemma event_O : (eventually O)->(Q O).
 Proof.
-Induction 1; Intros.
+NewInduction 1; Intros.
 Replace O with x; Auto with arith.
 Qed.