X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Fdrops_drops.ma;h=8549cf02a7e01f280f3e71ae656986b9a1056ca3;hp=68eddde1360c4544217a5dd8c064db27aa133380;hb=222044da28742b24584549ba86b1805a87def070;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
index 68eddde13..8549cf02a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
@@ -20,9 +20,9 @@ include "basic_2/relocation/drops_weight.ma".
 (* Main properties **********************************************************)
 
 (* Basic_2A1: includes: drop_conf_ge drop_conf_be drop_conf_le *)
-theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≡ L →
-                    ∀b2,f,L2. ⬇*[b2, f] L1 ≡ L2 →
-                    ∀f2. f1 ⊚ f2 ≡ f → ⬇*[b2, f2] L ≡ L2.
+theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L →
+                    ∀b2,f,L2. ⬇*[b2, f] L1 ≘ L2 →
+                    ∀f2. f1 ⊚ f2 ≘ f → ⬇*[b2, f2] L ≘ L2.
 #b1 #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #_ #b2 #f #L2 #HL2 #f2 #Hf12 elim (drops_inv_atom1 … HL2) -b1 -HL2
   #H #Hf destruct @drops_atom
@@ -41,9 +41,9 @@ qed-.
 (* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm 
                         drops_drop_trans
 *)
-theorem drops_trans: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≡ L →
-                     ∀b2,f2,L2. ⬇*[b2, f2] L ≡ L2 →
-                     ∀f. f1 ⊚ f2 ≡ f → ⬇*[b1∧b2, f] L1 ≡ L2.
+theorem drops_trans: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L →
+                     ∀b2,f2,L2. ⬇*[b2, f2] L ≘ L2 →
+                     ∀f. f1 ⊚ f2 ≘ f → ⬇*[b1∧b2, f] L1 ≘ L2.
 #b1 #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #Hf1 #b2 #f2 #L2 #HL2 #f #Hf elim (drops_inv_atom1 … HL2) -HL2
   #H #Hf2 destruct @drops_atom #H elim (andb_inv_true_dx … H) -H
@@ -59,8 +59,8 @@ theorem drops_trans: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≡ L →
 ]
 qed-.
 
-theorem drops_conf_div: ∀f1,L,K. ⬇*[Ⓣ,f1] L ≡ K → ∀f2. ⬇*[Ⓣ,f2] L ≡ K →
-                        𝐔⦃f1⦄ → 𝐔⦃f2⦄ → f1 ≗ f2.
+theorem drops_conf_div: ∀f1,L,K. ⬇*[Ⓣ,f1] L ≘ K → ∀f2. ⬇*[Ⓣ,f2] L ≘ K →
+                        𝐔⦃f1⦄ → 𝐔⦃f2⦄ → f1 ≡ f2.
 #f1 #L #K #H elim H -f1 -L -K
 [ #f1 #Hf1 #f2 #Hf2 elim (drops_inv_atom1 … Hf2) -Hf2
   /3 width=1 by isid_inv_eq_repl/
@@ -85,28 +85,28 @@ qed-.
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: includes: drop_mono *)
-lemma drops_mono: ∀b1,f,L,L1. ⬇*[b1, f] L ≡ L1 →
-                  ∀b2,L2. ⬇*[b2, f] L ≡ L2 → L1 = L2.
+lemma drops_mono: ∀b1,f,L,L1. ⬇*[b1, f] L ≘ L1 →
+                  ∀b2,L2. ⬇*[b2, f] L ≘ L2 → L1 = L2.
 #b1 #f #L #L1 lapply (after_isid_dx 𝐈𝐝 … f)
 /3 width=8 by drops_conf, drops_fwd_isid/
 qed-.
 
 (* Basic_2A1: includes: drop_conf_lt *)
-lemma drops_conf_skip1: ∀b2,f,L,L2. ⬇*[b2, f] L ≡ L2 →
-                        ∀b1,f1,I1,K1. ⬇*[b1, f1] L ≡ K1.ⓘ{I1} →
-                        ∀f2. f1 ⊚ ↑f2 ≡ f →
+lemma drops_conf_skip1: ∀b2,f,L,L2. ⬇*[b2, f] L ≘ L2 →
+                        ∀b1,f1,I1,K1. ⬇*[b1, f1] L ≘ K1.ⓘ{I1} →
+                        ∀f2. f1 ⊚ ⫯f2 ≘ f →
                         ∃∃I2,K2. L2 = K2.ⓘ{I2} &
-                                 ⬇*[b2, f2] K1 ≡ K2 & ⬆*[f2] I2 ≡ I1.
+                                 ⬇*[b2, f2] K1 ≘ K2 & ⬆*[f2] I2 ≘ I1.
 #b2 #f #L #L2 #H2 #b1 #f1 #I1 #K1 #H1 #f2 #Hf lapply (drops_conf … H1 … H2 … Hf) -L -Hf
 #H elim (drops_inv_skip1 … H) -H /2 width=5 by ex3_2_intro/
 qed-.
 
 (* Basic_2A1: includes: drop_trans_lt *)
-lemma drops_trans_skip2: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≡ L →
-                         ∀b2,f2,I2,K2. ⬇*[b2, f2] L ≡ K2.ⓘ{I2} →
-                         ∀f. f1 ⊚ f2 ≡ ↑f →
+lemma drops_trans_skip2: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L →
+                         ∀b2,f2,I2,K2. ⬇*[b2, f2] L ≘ K2.ⓘ{I2} →
+                         ∀f. f1 ⊚ f2 ≘ ⫯f →
                          ∃∃I1,K1. L1 = K1.ⓘ{I1} &
-                                  ⬇*[b1∧b2, f] K1 ≡ K2 & ⬆*[f] I2 ≡ I1.
+                                  ⬇*[b1∧b2, f] K1 ≘ K2 & ⬆*[f] I2 ≘ I1.
 #b1 #f1 #L1 #L #H1 #b2 #f2 #I2 #K2 #H2 #f #Hf
 lapply (drops_trans … H1 … H2 … Hf) -L -Hf
 #H elim (drops_inv_skip2 … H) -H /2 width=5 by ex3_2_intro/
@@ -114,8 +114,8 @@ qed-.
 
 (* Basic_2A1: includes: drops_conf_div *)
 lemma drops_conf_div_bind: ∀f1,f2,I1,I2,L,K.
-                           ⬇*[Ⓣ, f1] L ≡ K.ⓘ{I1} → ⬇*[Ⓣ, f2] L ≡ K.ⓘ{I2} →
-                           𝐔⦃f1⦄ → 𝐔⦃f2⦄ → f1 ≗ f2 ∧ I1 = I2.
+                           ⬇*[Ⓣ, f1] L ≘ K.ⓘ{I1} → ⬇*[Ⓣ, f2] L ≘ K.ⓘ{I2} →
+                           𝐔⦃f1⦄ → 𝐔⦃f2⦄ → f1 ≡ f2 ∧ I1 = I2.
 #f1 #f2 #I1 #I2 #L #K #Hf1 #Hf2 #HU1 #HU2
 lapply (drops_isuni_fwd_drop2 … Hf1) // #H1
 lapply (drops_isuni_fwd_drop2 … Hf2) // #H2
@@ -126,7 +126,7 @@ lapply (drops_mono … H0 … Hf2) -L #H
 destruct /2 width=1 by conj/
 qed-.
 
-lemma drops_inv_uni: ∀L,i. ⬇*[Ⓕ, 𝐔❴i❵] L ≡ ⋆ → ∀I,K. ⬇*[i] L ≡ K.ⓘ{I} → ⊥.
+lemma drops_inv_uni: ∀L,i. ⬇*[Ⓕ, 𝐔❴i❵] L ≘ ⋆ → ∀I,K. ⬇*[i] L ≘ K.ⓘ{I} → ⊥.
 #L #i #H1 #I #K #H2
 lapply (drops_F … H2) -H2 #H2
 lapply (drops_mono … H2 … H1) -L -i #H destruct