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[helm.git] / matita / matita / contribs / lambdadelta / static_2 / s_transition / fqu.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu.ma b/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu.ma
index bff7b2fe9e2561c7f349a58c358153d219d45d58..19dd4d45d0ab14148dbe2405d4f50b2b57ca9615 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu.ma
@@ -28,7 +28,7 @@ include "static_2/relocation/lifts.ma".
 inductive fqu (b:bool): tri_relation genv lenv term ≝
 | fqu_lref_O : ∀I,G,L,V. fqu b G (L.ⓑ{I}V) (#0) G L V
 | fqu_pair_sn: ∀I,G,L,V,T. fqu b G L (②{I}V.T) G L V
-| fqu_bind_dx: ∀p,I,G,L,V,T. fqu b G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
+| fqu_bind_dx: ∀p,I,G,L,V,T. b = Ⓣ → 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
@@ -44,24 +44,24 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma fqu_sort: â\88\80b,I,G,L,s. â¦\83G,L.â\93\98{I},â\8b\86sâ¦\84 â\8a\90[b] ⦃G,L,⋆s⦄.
+lemma fqu_sort: â\88\80b,I,G,L,s. â¦\83G,L.â\93\98{I},â\8b\86sâ¦\84 â¬\82[b] ⦃G,L,⋆s⦄.
 /2 width=1 by fqu_drop/ qed.
 
-lemma fqu_lref_S: â\88\80b,I,G,L,i. â¦\83G,L.â\93\98{I},#â\86\91iâ¦\84 â\8a\90[b] ⦃G,L,#i⦄.
+lemma fqu_lref_S: â\88\80b,I,G,L,i. â¦\83G,L.â\93\98{I},#â\86\91iâ¦\84 â¬\82[b] ⦃G,L,#i⦄.
 /2 width=1 by fqu_drop/ qed.
 
-lemma fqu_gref: â\88\80b,I,G,L,l. â¦\83G,L.â\93\98{I},§lâ¦\84 â\8a\90[b] ⦃G,L,§l⦄.
+lemma fqu_gref: â\88\80b,I,G,L,l. â¦\83G,L.â\93\98{I},§lâ¦\84 â¬\82[b] ⦃G,L,§l⦄.
 /2 width=1 by fqu_drop/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact fqu_inv_sort1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+fact fqu_inv_sort1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                         ∀s. T1 = ⋆s →
                         ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & T2 = ⋆s.
 #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #T #s #H destruct
 | #I #G #L #V #T #s #H destruct
-| #p #I #G #L #V #T #s #H destruct
+| #p #I #G #L #V #T #_ #s #H destruct
 | #p #I #G #L #V #T #_ #s #H destruct
 | #I #G #L #V #T #s #H destruct
 | #I #G #L #T #U #HI12 #s #H destruct
@@ -69,18 +69,18 @@ fact fqu_inv_sort1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G2,L2,T
 ]
 qed-.
 
-lemma fqu_inv_sort1: â\88\80b,G1,G2,L1,L2,T2,s. â¦\83G1,L1,â\8b\86sâ¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_sort1: â\88\80b,G1,G2,L1,L2,T2,s. â¦\83G1,L1,â\8b\86sâ¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                      ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & T2 = ⋆s.
 /2 width=4 by fqu_inv_sort1_aux/ qed-.
 
-fact fqu_inv_lref1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+fact fqu_inv_lref1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[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.
 #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
-| #p #I #G #L #V #T #i #H destruct
+| #p #I #G #L #V #T #_ #i #H destruct
 | #p #I #G #L #V #T #_ #i #H destruct
 | #I #G #L #V #T #i #H destruct
 | #I #G #L #T #U #HI12 #i #H destruct
@@ -88,18 +88,18 @@ fact fqu_inv_lref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G2,L2,T
 ]
 qed-.
 
-lemma fqu_inv_lref1: â\88\80b,G1,G2,L1,L2,T2,i. â¦\83G1,L1,#iâ¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_lref1: â\88\80b,G1,G2,L1,L2,T2,i. â¦\83G1,L1,#iâ¦\84 â¬\82[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.
 /2 width=4 by fqu_inv_lref1_aux/ qed-.
 
-fact fqu_inv_gref1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+fact fqu_inv_gref1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                         ∀l. T1 = §l →
                         ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & T2 = §l.
 #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #T #l #H destruct
 | #I #G #L #V #T #l #H destruct
-| #p #I #G #L #V #T #l #H destruct
+| #p #I #G #L #V #T #_ #l #H destruct
 | #p #I #G #L #V #T #_ #l #H destruct
 | #I #G #L #V #T #s #H destruct
 | #I #G #L #T #U #HI12 #l #H destruct
@@ -107,43 +107,44 @@ fact fqu_inv_gref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G2,L2,T
 ]
 qed-.
 
-lemma fqu_inv_gref1: â\88\80b,G1,G2,L1,L2,T2,l. â¦\83G1,L1,§lâ¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_gref1: â\88\80b,G1,G2,L1,L2,T2,l. â¦\83G1,L1,§lâ¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                      ∃∃J. G1 = G2 & L1 = L2.ⓘ{J} & T2 = §l.
 /2 width=4 by fqu_inv_gref1_aux/ qed-.
 
-fact fqu_inv_bind1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+fact fqu_inv_bind1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                         ∀p,I,V1,U1. T1 = ⓑ{p,I}V1.U1 →
                         ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
-                         | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2
+                         | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2 & b = Ⓣ
                          | ∧∧ G1 = G2 & L1.ⓧ = L2 & U1 = T2 & b = Ⓕ
                          | ∃∃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/
-| #p #I #G #L #V #T #q #J #V0 #U0 #H destruct /3 width=1 by and3_intro, or4_intro1/
+| #p #I #G #L #V #T #Hb #q #J #V0 #U0 #H destruct /3 width=1 by and4_intro, or4_intro1/
 | #p #I #G #L #V #T #Hb #q #J #V0 #U0 #H destruct /3 width=1 by and4_intro, or4_intro2/
 | #I #G #L #V #T #q #J #V0 #U0 #H destruct
 | #I #G #L #T #U #HTU #q #J #V0 #U0 #H destruct /3 width=2 by or4_intro3, ex3_intro/
 ]
 qed-.
 
-lemma fqu_inv_bind1: â\88\80b,p,I,G1,G2,L1,L2,V1,U1,T2. â¦\83G1,L1,â\93\91{p,I}V1.U1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_bind1: â\88\80b,p,I,G1,G2,L1,L2,V1,U1,T2. â¦\83G1,L1,â\93\91{p,I}V1.U1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                      ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
-                      | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2
+                      | ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2 & b = Ⓣ
                       | ∧∧ G1 = G2 & L1.ⓧ = L2 & U1 = T2 & b = Ⓕ
                       | ∃∃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: â\88\80p,I,G1,G2,L1,L2,V1,U1,T2. â¦\83G1,L1,â\93\91{p,I}V1.U1â¦\84 â\8a\90 ⦃G2,L2,T2⦄ →
+lemma fqu_inv_bind1_true: â\88\80p,I,G1,G2,L1,L2,V1,U1,T2. â¦\83G1,L1,â\93\91{p,I}V1.U1â¦\84 â¬\82 ⦃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.
 #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
+/3 width=1 by or3_intro0, or3_intro2/
+* #HG #HL #HU #H destruct
+/3 width=1 by and3_intro, or3_intro1/
 qed-.
 
-fact fqu_inv_flat1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+fact fqu_inv_flat1_aux: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                         ∀I,V1,U1. T1 = ⓕ{I}V1.U1 →
                         ∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
                          | ∧∧ G1 = G2 & L1 = L2 & U1 = T2
@@ -151,14 +152,14 @@ fact fqu_inv_flat1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G2,L2,T
 #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/
-| #p #I #G #L #V #T #J #V0 #U0 #H destruct
+| #p #I #G #L #V #T #_ #J #V0 #U0 #H destruct
 | #p #I #G #L #V #T #_ #J #V0 #U0 #H destruct
 | #I #G #L #V #T #J #V0 #U0 #H destruct /3 width=1 by and3_intro, or3_intro1/
 | #I #G #L #T #U #HTU #J #V0 #U0 #H destruct /3 width=2 by or3_intro2, ex3_intro/
 ]
 qed-.
 
-lemma fqu_inv_flat1: â\88\80b,I,G1,G2,L1,L2,V1,U1,T2. â¦\83G1,L1,â\93\95{I}V1.U1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_flat1: â\88\80b,I,G1,G2,L1,L2,V1,U1,T2. â¦\83G1,L1,â\93\95{I}V1.U1â¦\84 â¬\82[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.
@@ -166,31 +167,31 @@ lemma fqu_inv_flat1: ∀b,I,G1,G2,L1,L2,V1,U1,T2. ⦃G1,L1,ⓕ{I}V1.U1⦄ ⊐[b]
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma fqu_inv_atom1: â\88\80b,I,G1,G2,L2,T2. â¦\83G1,â\8b\86,â\93ª{I}â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ → ⊥.
+lemma fqu_inv_atom1: â\88\80b,I,G1,G2,L2,T2. â¦\83G1,â\8b\86,â\93ª{I}â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ → ⊥.
 #b * #x #G1 #G2 #L2 #T2 #H
 [ elim (fqu_inv_sort1 … H) | elim (fqu_inv_lref1 … H) * | elim (fqu_inv_gref1 … H) ] -H
 #I [2: #V |3: #i ] #_ #H destruct
 qed-.
 
-lemma fqu_inv_sort1_bind: â\88\80b,I,G1,G2,K,L2,T2,s. â¦\83G1,K.â\93\98{I},â\8b\86sâ¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_sort1_bind: â\88\80b,I,G1,G2,K,L2,T2,s. â¦\83G1,K.â\93\98{I},â\8b\86sâ¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                           ∧∧ G1 = G2 & L2 = K & T2 = ⋆s.
 #b #I #G1 #G2 #K #L2 #T2 #s #H elim (fqu_inv_sort1 … H) -H
 #Z #X #H1 #H2 destruct /2 width=1 by and3_intro/
 qed-.
 
-lemma fqu_inv_zero1_pair: â\88\80b,I,G1,G2,K,L2,V,T2. â¦\83G1,K.â\93\91{I}V,#0â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_zero1_pair: â\88\80b,I,G1,G2,K,L2,V,T2. â¦\83G1,K.â\93\91{I}V,#0â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                           ∧∧ G1 = G2 & L2 = K & T2 = V.
 #b #I #G1 #G2 #K #L2 #V #T2 #H elim (fqu_inv_lref1 … H) -H *
 #Z #X #H1 #H2 #H3 #H4 destruct /2 width=1 by and3_intro/
 qed-.
 
-lemma fqu_inv_lref1_bind: â\88\80b,I,G1,G2,K,L2,T2,i. â¦\83G1,K.â\93\98{I},#(â\86\91i)â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_lref1_bind: â\88\80b,I,G1,G2,K,L2,T2,i. â¦\83G1,K.â\93\98{I},#(â\86\91i)â¦\84 â¬\82[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/
 qed-.
 
-lemma fqu_inv_gref1_bind: â\88\80b,I,G1,G2,K,L2,T2,l. â¦\83G1,K.â\93\98{I},§lâ¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_inv_gref1_bind: â\88\80b,I,G1,G2,K,L2,T2,l. â¦\83G1,K.â\93\98{I},§lâ¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                           ∧∧ G1 = G2 & L2 = K & T2 = §l.
 #b #I #G1 #G2 #K #L2 #T2 #l #H elim (fqu_inv_gref1 … H) -H
 #Z #H1 #H2 #H3 destruct /2 width=1 by and3_intro/