update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / drops_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
index 1c44ed555a9e0956d3746e84c4cfc01972054393..b90bf07df102be28f7c7686bfb8e4a85e9d19b31 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
@@ -20,9 +20,9 @@ include "static_2/relocation/drops_weight.ma".
 (* Main properties **********************************************************)
 
 (* Basic_2A1: includes: drop_conf_ge drop_conf_be drop_conf_le *)
-theorem drops_conf: â\88\80b1,f1,L1,L. â¬\87*[b1, f1] L1 ≘ L →
-                    â\88\80b2,f,L2. â¬\87*[b2, f] L1 ≘ L2 →
-                    â\88\80f2. f1 â\8a\9a f2 â\89\98 f â\86\92 â¬\87*[b2, f2] L ≘ L2.
+theorem drops_conf: â\88\80b1,f1,L1,L. â\87©*[b1,f1] L1 ≘ L →
+                    â\88\80b2,f,L2. â\87©*[b2,f] L1 ≘ L2 →
+                    â\88\80f2. f1 â\8a\9a f2 â\89\98 f â\86\92 â\87©*[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
@@ -38,12 +38,12 @@ theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L →
 qed-.
 
 (* Basic_1: was: drop1_trans *)
-(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm 
+(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm
                         drops_drop_trans
 *)
-theorem drops_trans: â\88\80b1,f1,L1,L. â¬\87*[b1, f1] L1 ≘ L →
-                     â\88\80b2,f2,L2. â¬\87*[b2, f2] L ≘ L2 →
-                     â\88\80f. f1 â\8a\9a f2 â\89\98 f â\86\92 â¬\87*[b1â\88§b2, f] L1 ≘ L2.
+theorem drops_trans: â\88\80b1,f1,L1,L. â\87©*[b1,f1] L1 ≘ L →
+                     â\88\80b2,f2,L2. â\87©*[b2,f2] L ≘ L2 →
+                     â\88\80f. f1 â\8a\9a f2 â\89\98 f â\86\92 â\87©*[b1â\88§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: â\88\80f1,L,K. â¬\87*[â\93\89,f1] L â\89\98 K â\86\92 â\88\80f2. â¬\87*[Ⓣ,f2] L ≘ K →
-                        ð\9d\90\94â¦\83f1â¦\84 â\86\92 ð\9d\90\94â¦\83f2â¦\84 → f1 ≡ f2.
+theorem drops_conf_div: â\88\80f1,L,K. â\87©*[â\93\89,f1] L â\89\98 K â\86\92 â\88\80f2. â\87©*[Ⓣ,f2] L ≘ K →
+                        ð\9d\90\94â\9dªf1â\9d« â\86\92 ð\9d\90\94â\9dªf2â\9d« → 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 +85,42 @@ qed-.
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: includes: drop_mono *)
-lemma drops_mono: â\88\80b1,f,L,L1. â¬\87*[b1, f] L ≘ L1 →
-                  â\88\80b2,L2. â¬\87*[b2, f] L ≘ L2 → L1 = L2.
+lemma drops_mono: â\88\80b1,f,L,L1. â\87©*[b1,f] L ≘ L1 →
+                  â\88\80b2,L2. â\87©*[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-.
 
+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
+qed-.
+
+lemma drops_ldec_dec: ∀L,i. Decidable (∃∃K,W. ⇩*[i] L ≘ K.ⓛW).
+#L #i elim (drops_F_uni L i) [| * * [ #I #K1 | * #W1 #K1 ] ]
+[4: /3 width=3 by ex1_2_intro, or_introl/
+|*: #H1L @or_intror * #K2 #W2 #H2L
+    lapply (drops_mono … H2L … H1L) -L #H destruct
+]
+qed-.
+
 (* Basic_2A1: includes: drop_conf_lt *)
-lemma drops_conf_skip1: â\88\80b2,f,L,L2. â¬\87*[b2, f] L ≘ L2 →
-                        â\88\80b1,f1,I1,K1. â¬\87*[b1, f1] L â\89\98 K1.â\93\98{I1} →
+lemma drops_conf_skip1: â\88\80b2,f,L,L2. â\87©*[b2,f] L ≘ L2 →
+                        â\88\80b1,f1,I1,K1. â\87©*[b1,f1] L â\89\98 K1.â\93\98[I1] →
                         ∀f2. f1 ⊚ ⫯f2 ≘ f →
-                        ∃∃I2,K2. L2 = K2.ⓘ{I2} &
-                                 â¬\87*[b2, f2] K1 â\89\98 K2 & â¬\86*[f2] I2 ≘ I1.
+                        ∃∃I2,K2. L2 = K2.ⓘ[I2] &
+                                 â\87©*[b2,f2] K1 â\89\98 K2 & â\87§*[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: â\88\80b1,f1,L1,L. â¬\87*[b1, f1] L1 ≘ L →
-                         â\88\80b2,f2,I2,K2. â¬\87*[b2, f2] L â\89\98 K2.â\93\98{I2} →
+lemma drops_trans_skip2: â\88\80b1,f1,L1,L. â\87©*[b1,f1] L1 ≘ L →
+                         â\88\80b2,f2,I2,K2. â\87©*[b2,f2] L â\89\98 K2.â\93\98[I2] →
                          ∀f. f1 ⊚ f2 ≘ ⫯f →
-                         ∃∃I1,K1. L1 = K1.ⓘ{I1} &
-                                  â¬\87*[b1â\88§b2, f] K1 â\89\98 K2 & â¬\86*[f] I2 ≘ I1.
+                         ∃∃I1,K1. L1 = K1.ⓘ[I1] &
+                                  â\87©*[b1â\88§b2,f] K1 â\89\98 K2 & â\87§*[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 +128,8 @@ qed-.
 
 (* Basic_2A1: includes: drops_conf_div *)
 lemma drops_conf_div_bind: ∀f1,f2,I1,I2,L,K.
-                           â¬\87*[â\93\89, f1] L â\89\98 K.â\93\98{I1} â\86\92 â¬\87*[â\93\89, f2] L â\89\98 K.â\93\98{I2} →
-                           ð\9d\90\94â¦\83f1â¦\84 â\86\92 ð\9d\90\94â¦\83f2â¦\84 → f1 ≡ f2 ∧ I1 = I2.
+                           â\87©*[â\93\89,f1] L â\89\98 K.â\93\98[I1] â\86\92 â\87©*[â\93\89,f2] L â\89\98 K.â\93\98[I2] →
+                           ð\9d\90\94â\9dªf1â\9d« â\86\92 ð\9d\90\94â\9dªf2â\9d« → 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
@@ -125,9 +139,3 @@ lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0
 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} → ⊥.
-#L #i #H1 #I #K #H2
-lapply (drops_F … H2) -H2 #H2
-lapply (drops_mono … H2 … H1) -L -i #H destruct
-qed-.