renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubr_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr_drops.ma
index 5aa248fbc7af606a3c11e2855365590c19096bfb..f69618336444b10501d6957bba1844518950b816 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr_drops.ma
@@ -20,37 +20,33 @@ include "basic_2/static/lsubr.ma".
 (* Forward lemmas with generic slicing for local environments ***************)
 
 (* Basic_2A1: includes: lsubr_fwd_drop2_pair *)
-lemma lsubr_fwd_drops2_pair: ∀L1,L2. L1 ⫃ L2 → 
-                             ∀I,K2,W,c,f. 𝐔⦃f⦄ → ⬇*[c, f] L2 ≡ K2.ⓑ{I}W →
-                             (∃∃K1. K1 ⫃ K2 & ⬇*[c, f] L1 ≡ K1.ⓑ{I}W) ∨
-                             ∃∃K1,V. K1 ⫃ K2 & ⬇*[c, f] L1 ≡ K1.ⓓⓝW.V & I = Abst.
+lemma lsubr_fwd_drops2_bind: ∀L1,L2. L1 ⫃ L2 → 
+                             ∀b,f,I,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2.ⓘ{I} →
+                             ∨∨ ∃∃K1. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓘ{I}
+                              | ∃∃K1,W,V. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓓⓝW.V & I = BPair Abst W
+                              | ∃∃J1,J2,K1,V. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓑ{J1}V & I = BUnit J2.
 #L1 #L2 #H elim H -L1 -L2
-[ #L #I #K2 #W #c #f #_ #H
+[ #b #f #I #K2 #_ #H
   elim (drops_inv_atom1 … H) -H #H destruct
-| #J #L1 #L2 #V #HL12 #IH #I #K2 #W #c #f #Hf #H
-  elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
-  [ #Hf #H destruct -IH
-    /4 width=4 by drops_refl, ex2_intro, or_introl/
-  | #g #Hg #HLK2 #H destruct -HL12
-    elim (IH … Hg HLK2) -IH -Hg -HLK2 *
-    /4 width=4 by drops_drop, ex3_2_intro, ex2_intro, or_introl, or_intror/
-  ]
-| #L1 #L2 #V1 #V2 #HL12 #IH #I #K2 #W #c #f #Hf #H
-  elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
-  [ #Hf #H destruct -IH
-    /4 width=4 by drops_refl, ex3_2_intro, or_intror/
-  | #g #Hg #HLK2 #H destruct -HL12
-    elim (IH … Hg HLK2) -IH -Hg -HLK2 *
-    /4 width=4 by drops_drop, ex3_2_intro, ex2_intro, or_introl, or_intror/
-  ]
+| #J #L1 #L2 | #L1 #L2 #V #W | #I1 #I2 #L1 #L2 #V1
+]
+#HL12 #IH #b #f #I #K2 #Hf #H
+elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+[1,3,5: #Hf #H destruct -IH
+  /4 width=6 by drops_refl, or3_intro0, or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro, ex2_intro/
+|2,4,6: #g #Hg #HLK2 #H destruct -HL12
+  elim (IH … Hg HLK2) -IH -Hg -HLK2 *
+  /4 width=6 by drops_drop, or3_intro0, or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro, ex2_intro/
 ]
 qed-.
 
 (* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
 lemma lsubr_fwd_drops2_abbr: ∀L1,L2. L1 ⫃ L2 →
-                             ∀K2,V,c,f.  𝐔⦃f⦄ → ⬇*[c, f] L2 ≡ K2.ⓓV →
-                             ∃∃K1. K1 ⫃ K2 & ⬇*[c, f] L1 ≡ K1.ⓓV.
-#L1 #L2 #HL12 #K2 #V #c #f #Hf #HLK2
-elim (lsubr_fwd_drops2_pair … HL12 … Hf HLK2) -L2 -Hf // *
-#K1 #W #_ #_ #H destruct
+                             ∀b,f,K2,V.  𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2.ⓓV →
+                             ∃∃K1. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓓV.
+#L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
+elim (lsubr_fwd_drops2_bind … HL12 … Hf HLK2) -L2 -Hf // *
+[ #K1 #W #V #_ #_ #H destruct
+| #I1 #I2 #K1 #V #_ #_ #H destruct
+]
 qed-.