- "linear" flag added to lapply (automatic clearing)

[helm.git] / matita / contribs / RELATIONAL-ARITHMETICS / add_props.ma

diff --git a/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma b/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
index ab59c3a516a7846272400b16194e4128511775d4..dd360676b6cb464b9f98c8758ffcdc72a93129e3 100644 (file)
--- a/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
+++ b/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
@@ -22,9 +22,9 @@ qed.
 
 theorem add_S_1: \forall p,q,r. add p q r \to add (S p) q (S r).
  intros 2. elim q; clear q;
- [ lapply add_gen_O_2 to H as H0. clear H.
+ [ lapply linear add_gen_O_2 to H as H0.
    rewrite > H0. clear H0 p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
+ | lapply linear add_gen_S_2 to H1 as H0.
    decompose.
    rewrite > H2. clear H2 r
  ]; auto.
@@ -32,9 +32,9 @@ qed.
 
 theorem add_sym: \forall p,q,r. add p q r \to add q p r.
  intros 2. elim q; clear q;
- [ lapply add_gen_O_2 to H as H0. clear H.
+ [ lapply linear add_gen_O_2 to H as H0.
    rewrite > H0. clear H0 p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
+ | lapply linear add_gen_S_2 to H1 as H0.
    decompose.
    rewrite > H2. clear H2 r
  ]; auto.
@@ -42,7 +42,7 @@ qed.
 
 theorem add_shift_S_sx: \forall p,q,r. add p (S q) r \to add (S p) q r.
  intros.
- lapply add_gen_S_2 to H as H0. clear H.
+ lapply linear add_gen_S_2 to H as H0.
  decompose.
  rewrite > H1. clear H1 r.
  auto.
@@ -50,7 +50,7 @@ qed.
 
 theorem add_shift_S_dx: \forall p,q,r. add (S p) q r \to add p (S q) r.
  intros.
- lapply add_gen_S_1 to H as H0. clear H.
+ lapply linear add_gen_S_1 to H as H0.
  decompose.
  rewrite > H1. clear H1 r.
  auto.
@@ -60,15 +60,15 @@ theorem add_trans_1: \forall p,q1,r1. add p q1 r1 \to
                      \forall q2,r2. add r1 q2 r2 \to
                      \exists q. add q1 q2 q \land add p q r2.
  intros 2; elim q1; clear q1; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
+ [ lapply linear add_gen_O_2 to H as H0.
    rewrite > H0. clear H0 p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
+ | lapply linear add_gen_S_2 to H1 as H0.
    decompose.
    rewrite > H3. rewrite > H3 in H2. clear H3 r1.
-   lapply add_gen_S_1 to H2 as H0. clear H2.
+   lapply linear add_gen_S_1 to H2 as H0.
    decompose.
    rewrite > H2. clear H2 r2.
-   lapply H to H4, H3 as H0. clear H H4 H3.
+   lapply linear H to H4, H3 as H0.
    decompose.
  ]; apply ex_intro; [| auto || auto ]. (**)
 qed.
@@ -77,15 +77,15 @@ theorem add_trans_2: \forall p1,q,r1. add p1 q r1 \to
                      \forall p2,r2. add p2 r1 r2 \to
                      \exists p. add p1 p2 p \land add p q r2.
  intros 2; elim q; clear q; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
+ [ lapply linear add_gen_O_2 to H as H0.
    rewrite > H0. clear H0 p1
- | lapply add_gen_S_2 to H1 as H0. clear H1.
+ | lapply linear add_gen_S_2 to H1 as H0.
    decompose.
    rewrite > H3. rewrite > H3 in H2. clear H3 r1.
-   lapply add_gen_S_2 to H2 as H0. clear H2.
+   lapply linear add_gen_S_2 to H2 as H0.
    decompose.
    rewrite > H2. clear H2 r2.
-   lapply H to H4, H3 as H0. clear H H4 H3. 
+   lapply linear H to H4, H3 as H0.
    decompose.
  ]; apply ex_intro; [| auto || auto ]. (**)
 qed.
@@ -93,12 +93,12 @@ qed.
 theorem add_conf: \forall p,q,r1. add p q r1 \to 
                   \forall r2. add p q r2 \to r1 = r2.
  intros 2. elim q; clear q; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
+ [ lapply linear add_gen_O_2 to H as H0.
    rewrite > H0 in H1. clear H0 p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
+ | lapply linear add_gen_S_2 to H1 as H0.
    decompose.
    rewrite > H3. clear H3 r1.
-   lapply add_gen_S_2 to H2 as H0. clear H2.
+   lapply linear add_gen_S_2 to H2 as H0.
    decompose.
    rewrite > H2. clear H2 r2.
  ]; auto.