X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fs_computation%2Ffqus.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fs_computation%2Ffqus.ma;h=490e8e8a9101725d73b960a52e0165d2f6e8a1cf;hb=8ec019202bff90959cf1a7158b309e7f83fa222e;hp=3a58ae745433cb01d2e55f787bf89865e05a13cd;hpb=33d0a7a9029859be79b25b5a495e0f30dab11f37;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus.ma b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus.ma index 3a58ae745..490e8e8a9 100644 --- a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus.ma +++ b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus.ma @@ -34,15 +34,15 @@ interpretation "star-iterated structural successor (closure)" (* Basic eliminators ********************************************************) lemma fqus_ind: ∀b,G1,L1,T1. ∀Q:relation3 …. Q G1 L1 T1 → - (∀G,G2,L,L2,T,T2. ❪G1,L1,T1❫ ⬂*[b] ❪G,L,T❫ → ❪G,L,T❫ ⬂⸮[b] ❪G2,L2,T2❫ → Q G L T → Q G2 L2 T2) → - ∀G2,L2,T2. ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫ → Q G2 L2 T2. + (∀G,G2,L,L2,T,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G,L,T❩ → ❨G,L,T❩ ⬂⸮[b] ❨G2,L2,T2❩ → Q G L T → Q G2 L2 T2) → + ∀G2,L2,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩ → Q G2 L2 T2. #b #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H @(tri_TC_star_ind … IH1 IH2 G2 L2 T2 H) // qed-. lemma fqus_ind_dx: ∀b,G2,L2,T2. ∀Q:relation3 …. Q G2 L2 T2 → - (∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ⬂⸮[b] ❪G,L,T❫ → ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫ → Q G L T → Q G1 L1 T1) → - ∀G1,L1,T1. ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫ → Q G1 L1 T1. + (∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ⬂⸮[b] ❨G,L,T❩ → ❨G,L,T❩ ⬂*[b] ❨G2,L2,T2❩ → Q G L T → Q G1 L1 T1) → + ∀G1,L1,T1. ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩ → Q G1 L1 T1. #b #G2 #L2 #T2 #Q #IH1 #IH2 #G1 #L1 #T1 #H @(tri_TC_star_ind_dx … IH1 IH2 G1 L1 T1 H) // qed-. @@ -52,56 +52,56 @@ qed-. lemma fqus_refl: ∀b. tri_reflexive … (fqus b). /2 width=1 by tri_inj/ qed. -lemma fquq_fqus: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ → - ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fquq_fqus: ∀b,G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩ → + ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩. /2 width=1 by tri_inj/ qed. -lemma fqus_strap1: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ⬂*[b] ❪G,L,T❫ → - ❪G,L,T❫ ⬂⸮[b] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fqus_strap1: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G,L,T❩ → + ❨G,L,T❩ ⬂⸮[b] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩. /2 width=5 by tri_step/ qed-. -lemma fqus_strap2: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G,L,T❫ → - ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fqus_strap2: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G,L,T❩ → + ❨G,L,T❩ ⬂*[b] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩. /2 width=5 by tri_TC_strap/ qed-. (* Basic inversion lemmas ***************************************************) -lemma fqus_inv_fqu_sn: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_fqu_sn: ∀b,G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩ → (∧∧ G1 = G2 & L1 = L2 & T1 = T2) ∨ - ∃∃G,L,T. ❪G1,L1,T1❫ ⬂[b] ❪G,L,T❫ & ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫. + ∃∃G,L,T. ❨G1,L1,T1❩ ⬂[b] ❨G,L,T❩ & ❨G,L,T❩ ⬂*[b] ❨G2,L2,T2❩. #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 @(fqus_ind_dx … H12) -G1 -L1 -T1 /3 width=1 by and3_intro, or_introl/ #G1 #G #L1 #L #T1 #T * /3 width=5 by ex2_3_intro, or_intror/ * #HG #HL #HT #_ destruct // qed-. -lemma fqus_inv_sort1: ∀b,G1,G2,L1,L2,T2,s. ❪G1,L1,⋆s❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_sort1: ∀b,G1,G2,L1,L2,T2,s. ❨G1,L1,⋆s❩ ⬂*[b] ❨G2,L2,T2❩ → (∧∧ G1 = G2 & L1 = L2 & ⋆s = T2) ∨ - ∃∃J,L. ❪G1,L,⋆s❫ ⬂*[b] ❪G2,L2,T2❫ & L1 = L.ⓘ[J]. + ∃∃J,L. ❨G1,L,⋆s❩ ⬂*[b] ❨G2,L2,T2❩ & L1 = L.ⓘ[J]. #b #G1 #G2 #L1 #L2 #T2 #s #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/ #G #L #T #H elim (fqu_inv_sort1 … H) -H /3 width=4 by ex2_2_intro, or_intror/ qed-. -lemma fqus_inv_lref1: ∀b,G1,G2,L1,L2,T2,i. ❪G1,L1,#i❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_lref1: ∀b,G1,G2,L1,L2,T2,i. ❨G1,L1,#i❩ ⬂*[b] ❨G2,L2,T2❩ → ∨∨ ∧∧ G1 = G2 & L1 = L2 & #i = T2 - | ∃∃J,L,V. ❪G1,L,V❫ ⬂*[b] ❪G2,L2,T2❫ & L1 = L.ⓑ[J]V & i = 0 - | ∃∃J,L,j. ❪G1,L,#j❫ ⬂*[b] ❪G2,L2,T2❫ & L1 = L.ⓘ[J] & i = ↑j. + | ∃∃J,L,V. ❨G1,L,V❩ ⬂*[b] ❨G2,L2,T2❩ & L1 = L.ⓑ[J]V & i = 0 + | ∃∃J,L,j. ❨G1,L,#j❩ ⬂*[b] ❨G2,L2,T2❩ & L1 = L.ⓘ[J] & i = ↑j. #b #G1 #G2 #L1 #L2 #T2 #i #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or3_intro0/ #G #L #T #H elim (fqu_inv_lref1 … H) -H * /3 width=6 by ex3_3_intro, or3_intro1, or3_intro2/ qed-. -lemma fqus_inv_gref1: ∀b,G1,G2,L1,L2,T2,l. ❪G1,L1,§l❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_gref1: ∀b,G1,G2,L1,L2,T2,l. ❨G1,L1,§l❩ ⬂*[b] ❨G2,L2,T2❩ → (∧∧ G1 = G2 & L1 = L2 & §l = T2) ∨ - ∃∃J,L. ❪G1,L,§l❫ ⬂*[b] ❪G2,L2,T2❫ & L1 = L.ⓘ[J]. + ∃∃J,L. ❨G1,L,§l❩ ⬂*[b] ❨G2,L2,T2❩ & L1 = L.ⓘ[J]. #b #G1 #G2 #L1 #L2 #T2 #l #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/ #G #L #T #H elim (fqu_inv_gref1 … H) -H /3 width=4 by ex2_2_intro, or_intror/ qed-. -lemma fqus_inv_bind1: ∀b,p,I,G1,G2,L1,L2,V1,T1,T2. ❪G1,L1,ⓑ[p,I]V1.T1❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_bind1: ∀b,p,I,G1,G2,L1,L2,V1,T1,T2. ❨G1,L1,ⓑ[p,I]V1.T1❩ ⬂*[b] ❨G2,L2,T2❩ → ∨∨ ∧∧ G1 = G2 & L1 = L2 & ⓑ[p,I]V1.T1 = T2 - | ❪G1,L1,V1❫ ⬂*[b] ❪G2,L2,T2❫ - | ∧∧ ❪G1,L1.ⓑ[I]V1,T1❫ ⬂*[b] ❪G2,L2,T2❫ & b = Ⓣ - | ∧∧ ❪G1,L1.ⓧ,T1❫ ⬂*[b] ❪G2,L2,T2❫ & b = Ⓕ - | ∃∃J,L,T. ❪G1,L,T❫ ⬂*[b] ❪G2,L2,T2❫ & ⇧[1] T ≘ ⓑ[p,I]V1.T1 & L1 = L.ⓘ[J]. + | ❨G1,L1,V1❩ ⬂*[b] ❨G2,L2,T2❩ + | ∧∧ ❨G1,L1.ⓑ[I]V1,T1❩ ⬂*[b] ❨G2,L2,T2❩ & b = Ⓣ + | ∧∧ ❨G1,L1.ⓧ,T1❩ ⬂*[b] ❨G2,L2,T2❩ & b = Ⓕ + | ∃∃J,L,T. ❨G1,L,T❩ ⬂*[b] ❨G2,L2,T2❩ & ⇧[1] T ≘ ⓑ[p,I]V1.T1 & L1 = L.ⓘ[J]. #b #p #I #G1 #G2 #L1 #L2 #V1 #T1 #T2 #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or5_intro0/ #G #L #T #H elim (fqu_inv_bind1 … H) -H * [4: #J ] #H1 #H2 #H3 [3,4: #Hb ] #H destruct @@ -109,21 +109,21 @@ lemma fqus_inv_bind1: ∀b,p,I,G1,G2,L1,L2,V1,T1,T2. ❪G1,L1,ⓑ[p,I]V1.T1❫ qed-. -lemma fqus_inv_bind1_true: ∀p,I,G1,G2,L1,L2,V1,T1,T2. ❪G1,L1,ⓑ[p,I]V1.T1❫ ⬂* ❪G2,L2,T2❫ → +lemma fqus_inv_bind1_true: ∀p,I,G1,G2,L1,L2,V1,T1,T2. ❨G1,L1,ⓑ[p,I]V1.T1❩ ⬂* ❨G2,L2,T2❩ → ∨∨ ∧∧ G1 = G2 & L1 = L2 & ⓑ[p,I]V1.T1 = T2 - | ❪G1,L1,V1❫ ⬂* ❪G2,L2,T2❫ - | ❪G1,L1.ⓑ[I]V1,T1❫ ⬂* ❪G2,L2,T2❫ - | ∃∃J,L,T. ❪G1,L,T❫ ⬂* ❪G2,L2,T2❫ & ⇧[1] T ≘ ⓑ[p,I]V1.T1 & L1 = L.ⓘ[J]. + | ❨G1,L1,V1❩ ⬂* ❨G2,L2,T2❩ + | ❨G1,L1.ⓑ[I]V1,T1❩ ⬂* ❨G2,L2,T2❩ + | ∃∃J,L,T. ❨G1,L,T❩ ⬂* ❨G2,L2,T2❩ & ⇧[1] T ≘ ⓑ[p,I]V1.T1 & L1 = L.ⓘ[J]. #p #I #G1 #G2 #L1 #L2 #V1 #T1 #T2 #H elim (fqus_inv_bind1 … H) -H [1,3,4: * ] /3 width=1 by and3_intro, or4_intro0, or4_intro1, or4_intro2, or4_intro3/ #_ #H destruct qed-. -lemma fqus_inv_flat1: ∀b,I,G1,G2,L1,L2,V1,T1,T2. ❪G1,L1,ⓕ[I]V1.T1❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_flat1: ∀b,I,G1,G2,L1,L2,V1,T1,T2. ❨G1,L1,ⓕ[I]V1.T1❩ ⬂*[b] ❨G2,L2,T2❩ → ∨∨ ∧∧ G1 = G2 & L1 = L2 & ⓕ[I]V1.T1 = T2 - | ❪G1,L1,V1❫ ⬂*[b] ❪G2,L2,T2❫ - | ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫ - | ∃∃J,L,T. ❪G1,L,T❫ ⬂*[b] ❪G2,L2,T2❫ & ⇧[1] T ≘ ⓕ[I]V1.T1 & L1 = L.ⓘ[J]. + | ❨G1,L1,V1❩ ⬂*[b] ❨G2,L2,T2❩ + | ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩ + | ∃∃J,L,T. ❨G1,L,T❩ ⬂*[b] ❨G2,L2,T2❩ & ⇧[1] T ≘ ⓕ[I]V1.T1 & L1 = L.ⓘ[J]. #b #I #G1 #G2 #L1 #L2 #V1 #T1 #T2 #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or4_intro0/ #G #L #T #H elim (fqu_inv_flat1 … H) -H * [3: #J ] #H1 #H2 #H3 #H destruct @@ -132,35 +132,35 @@ qed-. (* Advanced inversion lemmas ************************************************) -lemma fqus_inv_atom1: ∀b,I,G1,G2,L2,T2. ❪G1,⋆,⓪[I]❫ ⬂*[b] ❪G2,L2,T2❫ → +lemma fqus_inv_atom1: ∀b,I,G1,G2,L2,T2. ❨G1,⋆,⓪[I]❩ ⬂*[b] ❨G2,L2,T2❩ → ∧∧ G1 = G2 & ⋆ = L2 & ⓪[I] = T2. #b #I #G1 #G2 #L2 #T2 #H elim (fqus_inv_fqu_sn … H) -H * /2 width=1 by and3_intro/ #G #L #T #H elim (fqu_inv_atom1 … H) qed-. -lemma fqus_inv_sort1_bind: ∀b,I,G1,G2,L1,L2,T2,s. ❪G1,L1.ⓘ[I],⋆s❫ ⬂*[b] ❪G2,L2,T2❫ → - (∧∧ G1 = G2 & L1.ⓘ[I] = L2 & ⋆s = T2) ∨ ❪G1,L1,⋆s❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fqus_inv_sort1_bind: ∀b,I,G1,G2,L1,L2,T2,s. ❨G1,L1.ⓘ[I],⋆s❩ ⬂*[b] ❨G2,L2,T2❩ → + (∧∧ G1 = G2 & L1.ⓘ[I] = L2 & ⋆s = T2) ∨ ❨G1,L1,⋆s❩ ⬂*[b] ❨G2,L2,T2❩. #b #I #G1 #G2 #L1 #L2 #T2 #s #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/ #G #L #T #H elim (fqu_inv_sort1_bind … H) -H #H1 #H2 #H3 #H destruct /2 width=1 by or_intror/ qed-. -lemma fqus_inv_zero1_pair: ∀b,I,G1,G2,L1,L2,V1,T2. ❪G1,L1.ⓑ[I]V1,#0❫ ⬂*[b] ❪G2,L2,T2❫ → - (∧∧ G1 = G2 & L1.ⓑ[I]V1 = L2 & #0 = T2) ∨ ❪G1,L1,V1❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fqus_inv_zero1_pair: ∀b,I,G1,G2,L1,L2,V1,T2. ❨G1,L1.ⓑ[I]V1,#0❩ ⬂*[b] ❨G2,L2,T2❩ → + (∧∧ G1 = G2 & L1.ⓑ[I]V1 = L2 & #0 = T2) ∨ ❨G1,L1,V1❩ ⬂*[b] ❨G2,L2,T2❩. #b #I #G1 #G2 #L1 #L2 #V1 #T2 #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/ #G #L #T #H elim (fqu_inv_zero1_pair … H) -H #H1 #H2 #H3 #H destruct /2 width=1 by or_intror/ qed-. -lemma fqus_inv_lref1_bind: ∀b,I,G1,G2,L1,L2,T2,i. ❪G1,L1.ⓘ[I],#↑i❫ ⬂*[b] ❪G2,L2,T2❫ → - (∧∧ G1 = G2 & L1.ⓘ[I] = L2 & #(↑i) = T2) ∨ ❪G1,L1,#i❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fqus_inv_lref1_bind: ∀b,I,G1,G2,L1,L2,T2,i. ❨G1,L1.ⓘ[I],#↑i❩ ⬂*[b] ❨G2,L2,T2❩ → + (∧∧ G1 = G2 & L1.ⓘ[I] = L2 & #(↑i) = T2) ∨ ❨G1,L1,#i❩ ⬂*[b] ❨G2,L2,T2❩. #b #I #G1 #G2 #L1 #L2 #T2 #i #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/ #G #L #T #H elim (fqu_inv_lref1_bind … H) -H #H1 #H2 #H3 #H destruct /2 width=1 by or_intror/ qed-. -lemma fqus_inv_gref1_bind: ∀b,I,G1,G2,L1,L2,T2,l. ❪G1,L1.ⓘ[I],§l❫ ⬂*[b] ❪G2,L2,T2❫ → - (∧∧ G1 = G2 & L1.ⓘ[I] = L2 & §l = T2) ∨ ❪G1,L1,§l❫ ⬂*[b] ❪G2,L2,T2❫. +lemma fqus_inv_gref1_bind: ∀b,I,G1,G2,L1,L2,T2,l. ❨G1,L1.ⓘ[I],§l❩ ⬂*[b] ❨G2,L2,T2❩ → + (∧∧ G1 = G2 & L1.ⓘ[I] = L2 & §l = T2) ∨ ❨G1,L1,§l❩ ⬂*[b] ❨G2,L2,T2❩. #b #I #G1 #G2 #L1 #L2 #T2 #l #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/ #G #L #T #H elim (fqu_inv_gref1_bind … H) -H #H1 #H2 #H3 #H destruct /2 width=1 by or_intror/