X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fs_transition%2Ffqu.ma;h=0377df1a1af7d2e76d36b7090547b62a220283cb;hp=8dcfa103d10e4bd0a8f9b529675039be8527c153;hb=222044da28742b24584549ba86b1805a87def070;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.ma b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.ma
index 8dcfa103d..0377df1a1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.ma
@@ -31,7 +31,7 @@ inductive fqu (b:bool): tri_relation genv lenv term ≝
 | fqu_bind_dx: ∀p,I,G,L,V,T. fqu b G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
 | fqu_clear  : ∀p,I,G,L,V,T. b = Ⓕ → fqu b G L (ⓑ{p,I}V.T) G (L.ⓧ) T
 | fqu_flat_dx: ∀I,G,L,V,T. fqu b G L (ⓕ{I}V.T) G L T
-| fqu_drop   : ∀I,G,L,T,U. ⬆*[1] T ≡ U → fqu b G (L.ⓘ{I}) U G L T
+| fqu_drop   : ∀I,G,L,T,U. ⬆*[1] T ≘ U → fqu b G (L.ⓘ{I}) U G L T
 .
 
 interpretation
@@ -44,7 +44,13 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma fqu_lref_S: ∀b,I,G,L,V,i. ⦃G, L.ⓑ{I}V, #⫯i⦄ ⊐[b] ⦃G, L, #i⦄.
+lemma fqu_sort: ∀b,I,G,L,s. ⦃G, L.ⓘ{I}, ⋆s⦄ ⊐[b] ⦃G, L, ⋆s⦄.
+/2 width=1 by fqu_drop/ qed.
+
+lemma fqu_lref_S: ∀b,I,G,L,i. ⦃G, L.ⓘ{I}, #↑i⦄ ⊐[b] ⦃G, L, #i⦄.
+/2 width=1 by fqu_drop/ qed.
+
+lemma fqu_gref: ∀b,I,G,L,l. ⦃G, L.ⓘ{I}, §l⦄ ⊐[b] ⦃G, L, §l⦄.
 /2 width=1 by fqu_drop/ qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -70,7 +76,7 @@ lemma fqu_inv_sort1: ∀b,G1,G2,L1,L2,T2,s. ⦃G1, L1, ⋆s⦄ ⊐[b] ⦃G2, L2,
 fact fqu_inv_lref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                         ∀i. T1 = #i →
                         (∃∃J,V. G1 = G2 & L1 = L2.ⓑ{J}V & T2 = V & i = 0) ∨
-                        ∃∃J,j. G1 = G2 & L1 = L2.ⓘ{J} & T2 = #j & i = ⫯j.
+                        ∃∃J,j. G1 = G2 & L1 = L2.ⓘ{J} & T2 = #j & i = ↑j.
 #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #T #i #H destruct /3 width=4 by ex4_2_intro, or_introl/
 | #I #G #L #V #T #i #H destruct
@@ -84,7 +90,7 @@ qed-.
 
 lemma fqu_inv_lref1: ∀b,G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                      (∃∃J,V. G1 = G2 & L1 = L2.ⓑ{J}V & T2 = V & i = 0) ∨
-                     ∃∃J,j. G1 = G2 & L1 = L2.ⓘ{J} & T2 = #j & i = ⫯j.
+                     ∃∃J,j. G1 = G2 & L1 = L2.ⓘ{J} & T2 = #j & i = ↑j.
 /2 width=4 by fqu_inv_lref1_aux/ qed-.
 
 fact fqu_inv_gref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
@@ -110,7 +116,7 @@ fact fqu_inv_bind1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L
                         ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
                          | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2
                          | ∧∧ G1 = G2 & L1.ⓧ = L2 & U1 = T2 & b = Ⓕ
-                         | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≡ ⓑ{p,I}V1.U1.
+                         | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≘ ⓑ{p,I}V1.U1.
 #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #T #q #J #V0 #U0 #H destruct
 | #I #G #L #V #T #q #J #V0 #U0 #H destruct /3 width=1 by and3_intro, or4_intro0/
@@ -125,13 +131,13 @@ lemma fqu_inv_bind1: ∀b,p,I,G1,G2,L1,L2,V1,U1,T2. ⦃G1, L1, ⓑ{p,I}V1.U1⦄
                      ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
                       | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2
                       | ∧∧ G1 = G2 & L1.ⓧ = L2 & U1 = T2 & b = Ⓕ
-                      | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≡ ⓑ{p,I}V1.U1.
+                      | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≘ ⓑ{p,I}V1.U1.
 /2 width=4 by fqu_inv_bind1_aux/ qed-.
 
 lemma fqu_inv_bind1_true: ∀p,I,G1,G2,L1,L2,V1,U1,T2. ⦃G1, L1, ⓑ{p,I}V1.U1⦄ ⊐ ⦃G2, L2, T2⦄ →
                           ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
                            | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2
-                           | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≡ ⓑ{p,I}V1.U1.
+                           | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≘ ⓑ{p,I}V1.U1.
 #p #I #G1 #G2 #L1 #L2 #V1 #U1 #T2 #H elim (fqu_inv_bind1 … H) -H
 /3 width=1 by or3_intro0, or3_intro1, or3_intro2/
 * #_ #_ #_ #H destruct
@@ -141,7 +147,7 @@ fact fqu_inv_flat1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L
                         ∀I,V1,U1. T1 = ⓕ{I}V1.U1 →
                         ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
                          | ∧∧ G1 = G2 & L1 = L2 & U1 = T2
-                         | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≡ ⓕ{I}V1.U1.
+                         | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≘ ⓕ{I}V1.U1.
 #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #T #J #V0 #U0 #H destruct
 | #I #G #L #V #T #J #V0 #U0 #H destruct /3 width=1 by and3_intro, or3_intro0/
@@ -155,7 +161,7 @@ qed-.
 lemma fqu_inv_flat1: ∀b,I,G1,G2,L1,L2,V1,U1,T2. ⦃G1, L1, ⓕ{I}V1.U1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                      ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
                       | ∧∧ G1 = G2 & L1 = L2 & U1 = T2
-                      | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≡ ⓕ{I}V1.U1.
+                      | ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & ⬆*[1] T2 ≘ ⓕ{I}V1.U1.
 /2 width=4 by fqu_inv_flat1_aux/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
@@ -178,7 +184,7 @@ lemma fqu_inv_zero1_pair: ∀b,I,G1,G2,K,L2,V,T2. ⦃G1, K.ⓑ{I}V, #0⦄ ⊐[b]
 #Z #X #H1 #H2 #H3 #H4 destruct /2 width=1 by and3_intro/
 qed-.
 
-lemma fqu_inv_lref1_bind: ∀b,I,G1,G2,K,L2,T2,i. ⦃G1, K.ⓘ{I}, #(⫯i)⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+lemma fqu_inv_lref1_bind: ∀b,I,G1,G2,K,L2,T2,i. ⦃G1, K.ⓘ{I}, #(↑i)⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                           ∧∧ G1 = G2 & L2 = K & T2 = #i.
 #b #I #G1 #G2 #K #L2 #T2 #i #H elim (fqu_inv_lref1 … H) -H *
 #Z #X #H1 #H2 #H3 #H4 destruct /2 width=1 by and3_intro/