update in static_2 and basic_2 for the article

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rdeq.ma b/matita/matita/contribs/lambdadelta/static_2/static/rdeq.ma
index 6cb56dcaf43200dc2c6eebb6751107f973902db0..99fe14ee67f675b34df0f6b722ec822d8497f057 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rdeq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rdeq.ma
@@ -31,8 +31,8 @@ interpretation
 
 (* Basic properties ***********************************************************)
 
-lemma frees_tdeq_conf_rdeq: ∀f,L1,T1. L1 ⊢ 𝐅*⦃T1⦄ ≘ f → ∀T2. T1 ≛ T2 →
-                            ∀L2. L1 ≛[f] L2 → L2 ⊢ 𝐅*⦃T2⦄ ≘ f.
+lemma frees_tdeq_conf_rdeq: ∀f,L1,T1. L1 ⊢ 𝐅+⦃T1⦄ ≘ f → ∀T2. T1 ≛ T2 →
+                            ∀L2. L1 ≛[f] L2 → L2 ⊢ 𝐅+⦃T2⦄ ≘ f.
 #f #L1 #T1 #H elim H -f -L1 -T1
 [ #f #L1 #s1 #Hf #X #H1 #L2 #_
   elim (tdeq_inv_sort1 … H1) -H1 #s2 #H destruct
@@ -65,12 +65,12 @@ lemma frees_tdeq_conf_rdeq: ∀f,L1,T1. L1 ⊢ 𝐅*⦃T1⦄ ≘ f → ∀T2. T1
 ]
 qed-.
 
-lemma frees_tdeq_conf: ∀f,L,T1. L ⊢ 𝐅*⦃T1⦄ ≘ f →
-                       ∀T2. T1 ≛ T2 → L ⊢ 𝐅*⦃T2⦄ ≘ f.
+lemma frees_tdeq_conf: ∀f,L,T1. L ⊢ 𝐅+⦃T1⦄ ≘ f →
+                       ∀T2. T1 ≛ T2 → L ⊢ 𝐅+⦃T2⦄ ≘ f.
 /4 width=7 by frees_tdeq_conf_rdeq, sex_refl, ext2_refl/ qed-.
 
-lemma frees_rdeq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≘ f →
-                       ∀L2. L1 ≛[f] L2 → L2 ⊢ 𝐅*⦃T⦄ ≘ f.
+lemma frees_rdeq_conf: ∀f,L1,T. L1 ⊢ 𝐅+⦃T⦄ ≘ f →
+                       ∀L2. L1 ≛[f] L2 → L2 ⊢ 𝐅+⦃T⦄ ≘ f.
 /2 width=7 by frees_tdeq_conf_rdeq, tdeq_refl/ qed-.
 
 lemma tdeq_rex_conf (R): s_r_confluent1 … cdeq (rex R).
@@ -79,7 +79,7 @@ lemma tdeq_rex_conf (R): s_r_confluent1 … cdeq (rex R).
 qed-.
 
 lemma tdeq_rex_div (R): ∀T1,T2. T1 ≛ T2 →
-                        ∀L1,L2. L1 ⪤[R, T2] L2 → L1 ⪤[R, T1] L2.
+                        ∀L1,L2. L1 ⪤[R,T2] L2 → L1 ⪤[R,T1] L2.
 /3 width=5 by tdeq_rex_conf, tdeq_sym/ qed-.
 
 lemma tdeq_rdeq_conf: s_r_confluent1 … cdeq rdeq.
@@ -99,11 +99,11 @@ lemma rdeq_sort: ∀I1,I2,L1,L2,s.
 lemma rdeq_pair: ∀I,L1,L2,V1,V2.
                  L1 ≛[V1] L2 → V1 ≛ V2 → L1.ⓑ{I}V1 ≛[#0] L2.ⓑ{I}V2.
 /2 width=1 by rex_pair/ qed.
-(*
-lemma rdeq_unit: â\88\80f,I,L1,L2. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L1 ⪤[cdeq_ext, cfull, f] L2 →
+
+lemma rdeq_unit: â\88\80f,I,L1,L2. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L1 â\89\9b[f] L2 →
                  L1.ⓤ{I} ≛[#0] L2.ⓤ{I}.
 /2 width=3 by rex_unit/ qed.
-*)
+
 lemma rdeq_lref: ∀I1,I2,L1,L2,i.
                  L1 ≛[#i] L2 → L1.ⓘ{I1} ≛[#↑i] L2.ⓘ{I2}.
 /2 width=1 by rex_lref/ qed.
@@ -125,17 +125,16 @@ lemma rdeq_inv_atom_sn: ∀Y2. ∀T:term. ⋆ ≛[T] Y2 → Y2 = ⋆.
 
 lemma rdeq_inv_atom_dx: ∀Y1. ∀T:term. Y1 ≛[T] ⋆ → Y1 = ⋆.
 /2 width=3 by rex_inv_atom_dx/ qed-.
-(*
-lemma rdeq_inv_zero: ∀Y1,Y2. Y1 ≛[#0] Y2 →
-                     ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
-                      | ∃∃I,L1,L2,V1,V2. L1 ≛[V1] L2 & V1 ≛ V2 &
-                                         Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
-                      | ∃∃f,I,L1,L2. 𝐈⦃f⦄ & L1 ⪤[cdeq_ext h o, cfull, f] L2 &
-                                         Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+
+lemma rdeq_inv_zero:
+      ∀Y1,Y2. Y1 ≛[#0] Y2 →
+      ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+       | ∃∃I,L1,L2,V1,V2. L1 ≛[V1] L2 & V1 ≛ V2 & Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
+       | ∃∃f,I,L1,L2. 𝐈⦃f⦄ & L1 ≛[f] L2 & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
 #Y1 #Y2 #H elim (rex_inv_zero … H) -H *
 /3 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex4_4_intro, conj/
 qed-.
-*)
+
 lemma rdeq_inv_lref: ∀Y1,Y2,i. Y1 ≛[#↑i] Y2 →
                      ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
                       | ∃∃I1,I2,L1,L2. L1 ≛[#i] L2 &