- fpbg can be reflexive (example given)

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / lleq_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_lleq.ma
index 0458e1da887517e4983a9f0afbf96e63ee38de46..d07e13fce79796a39fe68966d16160d7e64a8f57 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_lleq.ma
@@ -14,6 +14,8 @@
 
 include "basic_2/multiple/lleq_drop.ma".
 
+(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
+
 (* Main properties **********************************************************)
 
 theorem lleq_trans: ∀d,T. Transitive … (lleq d T).
@@ -25,8 +27,13 @@ theorem lleq_canc_sn: ∀L,L1,L2,T,d. L ≡[d, T] L1→ L ≡[d, T] L2 → L1 
 theorem lleq_canc_dx: ∀L1,L2,L,T,d. L1 ≡[d, T] L → L2 ≡[d, T] L → L1 ≡[d, T] L2.
 /3 width=3 by lleq_trans, lleq_sym/ qed-.
 
-(* Note: lleq_nlleq_trans: ∀d,T,L1,L. L1≡[T, d] L →
-                           ∀L2. (L ≡[T, d] L2 → ⊥) → (L1 ≡[T, d] L2 → ⊥).
+(* Advanced properies on negated lazy equivalence *****************************)
+
+(* Note: for use in auto, works with /4 width=8/ so lleq_canc_sn is preferred *) 
+lemma lleq_nlleq_trans: ∀d,T,L1,L. L1 ≡[T, d] L →
+                        ∀L2. (L ≡[T, d] L2 → ⊥) → (L1 ≡[T, d] L2 → ⊥).
 /3 width=3 by lleq_canc_sn/ qed-.
-works with /4 width=8/ so lleq_canc_sn is more convenient
-*)
+
+lemma nlleq_lleq_div: ∀d,T,L2,L. L2 ≡[T, d] L →
+                      ∀L1. (L1 ≡[T, d] L → ⊥) → (L1 ≡[T, d] L2 → ⊥).
+/3 width=3 by lleq_trans/ qed-.