X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfdeq_lfdeq.ma;h=2edd66b91710474d0e2364d90cd7252b1803fd4b;hb=6167cca50de37eba76a062537b24f7caef5b34f2;hp=92f66ba6112a8598d4899b7881ef2461695d5664;hpb=6d49221c1fefe6a2c5bddb3db24d3698414a700f;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma
index 92f66ba61..2edd66b91 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma
@@ -22,25 +22,25 @@ include "basic_2/static/lfdeq.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: lleq_dec *)
-lemma lfdeq_dec: ∀h,o,L1,L2. ∀T:term. Decidable (L1 ≡[h, o, T] L2).
+lemma lfdeq_dec: ∀h,o,L1,L2. ∀T:term. Decidable (L1 ≛[h, o, T] L2).
 /3 width=1 by lfxs_dec, tdeq_dec/ qed-.
 
 (* Main properties **********************************************************)
 
 (* Basic_2A1: uses: lleq_bind lleq_bind_O *) 
 theorem lfdeq_bind: ∀h,o,p,I,L1,L2,V1,V2,T.
-                    L1 ≡[h, o, V1] L2 → L1.ⓑ{I}V1 ≡[h, o, T] L2.ⓑ{I}V2 →
-                    L1 ≡[h, o, ⓑ{p,I}V1.T] L2.
+                    L1 ≛[h, o, V1] L2 → L1.ⓑ{I}V1 ≛[h, o, T] L2.ⓑ{I}V2 →
+                    L1 ≛[h, o, ⓑ{p,I}V1.T] L2.
 /2 width=2 by lfxs_bind/ qed.
 
 (* Basic_2A1: uses: lleq_flat *)
-theorem lfdeq_flat: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, V] L2 → L1 ≡[h, o, T] L2 →
-                    L1 ≡[h, o, ⓕ{I}V.T] L2.
+theorem lfdeq_flat: ∀h,o,I,L1,L2,V,T. L1 ≛[h, o, V] L2 → L1 ≛[h, o, T] L2 →
+                    L1 ≛[h, o, ⓕ{I}V.T] L2.
 /2 width=1 by lfxs_flat/ qed.
 
 theorem lfdeq_bind_void: ∀h,o,p,I,L1,L2,V,T.
-                         L1 ≡[h, o, V] L2 → L1.ⓧ ≡[h, o, T] L2.ⓧ →
-                         L1 ≡[h, o, ⓑ{p,I}V.T] L2.
+                         L1 ≛[h, o, V] L2 → L1.ⓧ ≛[h, o, T] L2.ⓧ →
+                         L1 ≛[h, o, ⓑ{p,I}V.T] L2.
 /2 width=1 by lfxs_bind_void/ qed.
 
 (* Basic_2A1: uses: lleq_trans *)
@@ -59,39 +59,39 @@ theorem lfdeq_canc_sn: ∀h,o,T. left_cancellable … (lfdeq h o T).
 theorem lfdeq_canc_dx: ∀h,o,T. right_cancellable … (lfdeq h o T).
 /3 width=3 by lfdeq_trans, lfdeq_sym/ qed-.
 
-theorem lfdeq_repl: ∀h,o,L1,L2. ∀T:term. L1 ≡[h, o, T] L2 →
-                    ∀K1. L1 ≡[h, o, T] K1 → ∀K2. L2 ≡[h, o, T] K2 → K1 ≡[h, o, T] K2.
+theorem lfdeq_repl: ∀h,o,L1,L2. ∀T:term. L1 ≛[h, o, T] L2 →
+                    ∀K1. L1 ≛[h, o, T] K1 → ∀K2. L2 ≛[h, o, T] K2 → K1 ≛[h, o, T] K2.
 /3 width=3 by lfdeq_canc_sn, lfdeq_trans/ qed-.
 
 (* Negated properties *******************************************************)
 
 (* Note: auto works with /4 width=8/ so lfdeq_canc_sn is preferred **********) 
 (* Basic_2A1: uses: lleq_nlleq_trans *)
-lemma lfdeq_lfdneq_trans: ∀h,o.∀T:term.∀L1,L. L1 ≡[h, o, T] L →
-                          ∀L2. (L ≡[h, o, T] L2 → ⊥) → (L1 ≡[h, o, T] L2 → ⊥).
+lemma lfdeq_lfdneq_trans: ∀h,o.∀T:term.∀L1,L. L1 ≛[h, o, T] L →
+                          ∀L2. (L ≛[h, o, T] L2 → ⊥) → (L1 ≛[h, o, T] L2 → ⊥).
 /3 width=3 by lfdeq_canc_sn/ qed-.
 
 (* Basic_2A1: uses: nlleq_lleq_div *)
-lemma lfdneq_lfdeq_div: ∀h,o.∀T:term.∀L2,L. L2 ≡[h, o, T] L →
-                        ∀L1. (L1 ≡[h, o, T] L → ⊥) → (L1 ≡[h, o, T] L2 → ⊥).
+lemma lfdneq_lfdeq_div: ∀h,o.∀T:term.∀L2,L. L2 ≛[h, o, T] L →
+                        ∀L1. (L1 ≛[h, o, T] L → ⊥) → (L1 ≛[h, o, T] L2 → ⊥).
 /3 width=3 by lfdeq_trans/ qed-.
 
-theorem lfdneq_lfdeq_canc_dx: ∀h,o,L1,L. ∀T:term. (L1 ≡[h, o, T] L → ⊥) →
-                              ∀L2. L2 ≡[h, o, T] L → L1 ≡[h, o, T] L2 → ⊥.
+theorem lfdneq_lfdeq_canc_dx: ∀h,o,L1,L. ∀T:term. (L1 ≛[h, o, T] L → ⊥) →
+                              ∀L2. L2 ≛[h, o, T] L → L1 ≛[h, o, T] L2 → ⊥.
 /3 width=3 by lfdeq_trans/ qed-.
 
 (* Negated inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: nlleq_inv_bind nlleq_inv_bind_O *)
-lemma lfdneq_inv_bind: ∀h,o,p,I,L1,L2,V,T. (L1 ≡[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
-                       (L1 ≡[h, o, V] L2 → ⊥) ∨ (L1.ⓑ{I}V ≡[h, o, T] L2.ⓑ{I}V → ⊥).
+lemma lfdneq_inv_bind: ∀h,o,p,I,L1,L2,V,T. (L1 ≛[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
+                       (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1.ⓑ{I}V ≛[h, o, T] L2.ⓑ{I}V → ⊥).
 /3 width=2 by lfnxs_inv_bind, tdeq_dec/ qed-.
 
 (* Basic_2A1: uses: nlleq_inv_flat *)
-lemma lfdneq_inv_flat: ∀h,o,I,L1,L2,V,T. (L1 ≡[h, o, ⓕ{I}V.T] L2 → ⊥) →
-                       (L1 ≡[h, o, V] L2 → ⊥) ∨ (L1 ≡[h, o, T] L2 → ⊥).
+lemma lfdneq_inv_flat: ∀h,o,I,L1,L2,V,T. (L1 ≛[h, o, ⓕ{I}V.T] L2 → ⊥) →
+                       (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1 ≛[h, o, T] L2 → ⊥).
 /3 width=2 by lfnxs_inv_flat, tdeq_dec/ qed-.
 
-lemma lfdneq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. (L1 ≡[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
-                            (L1 ≡[h, o, V] L2 → ⊥) ∨ (L1.ⓧ ≡[h, o, T] L2.ⓧ → ⊥).
+lemma lfdneq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. (L1 ≛[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
+                            (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1.ⓧ ≛[h, o, T] L2.ⓧ → ⊥).
 /3 width=3 by lfnxs_inv_bind_void, tdeq_dec/ qed-.