X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpg_drops.ma;h=a98e061f39d5a61c872c36ca97cf219d573453f3;hp=295cc229125f35c25126ff498229fc7e1458abb4;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hpb=4ce795bb1d356e2565c14087b933adaccfc81dcd diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma index 295cc2291..a98e061f3 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma @@ -12,32 +12,32 @@ (* *) (**************************************************************************) -include "basic_2/relocation/drops_drops.ma". -include "basic_2/s_computation/fqup_weight.ma". -include "basic_2/s_computation/fqup_drops.ma". +include "static_2/relocation/drops_drops.ma". +include "static_2/s_computation/fqup_weight.ma". +include "static_2/s_computation/fqup_drops.ma". include "basic_2/rt_transition/cpg.ma". -(* COUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************) +(* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************) (* Advanced properties ******************************************************) -lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ⬈[Rt, c, h] V2 → - ⬆*[⫯i] V2 ≡ T2 → ⦃G, L⦄ ⊢ #i ⬈[Rt, c, h] T2. +lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≘ K.ⓓV → ⦃G, K⦄ ⊢ V ⬈[Rt, c, h] V2 → + ⬆*[↑i] V2 ≘ T2 → ⦃G, L⦄ ⊢ #i ⬈[Rt, c, h] T2. #Rt #c #h #G #K #V #V2 #i elim i -i [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_delta/ | #i #IH #L0 #T0 #H0 #HV2 #HVT2 elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct - elim (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ + elim (lifts_split_trans … HVT2 (𝐔❴↑i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ ] qed. -lemma cpg_ell_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓛV → ⦃G, K⦄ ⊢ V ⬈[Rt,c, h] V2 → - ⬆*[⫯i] V2 ≡ T2 → ⦃G, L⦄ ⊢ #i ⬈[Rt, c+𝟘𝟙, h] T2. +lemma cpg_ell_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≘ K.ⓛV → ⦃G, K⦄ ⊢ V ⬈[Rt,c, h] V2 → + ⬆*[↑i] V2 ≘ T2 → ⦃G, L⦄ ⊢ #i ⬈[Rt, c+𝟘𝟙, h] T2. #Rt #c #h #G #K #V #V2 #i elim i -i [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_ell/ | #i #IH #L0 #T0 #H0 #HV2 #HVT2 elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct - elim (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ + elim (lifts_split_trans … HVT2 (𝐔❴↑i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/ ] qed. @@ -45,10 +45,10 @@ qed. lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2 → ∨∨ T2 = #i ∧ c = 𝟘𝟘 - | ∃∃cV,K,V,V2. ⬇*[i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & - ⬆*[⫯i] V2 ≡ T2 & c = cV - | ∃∃cV,K,V,V2. ⬇*[i] L ≡ K.ⓛV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & - ⬆*[⫯i] V2 ≡ T2 & c = cV + 𝟘𝟙. + | ∃∃cV,K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & + ⬆*[↑i] V2 ≘ T2 & c = cV + | ∃∃cV,K,V,V2. ⬇*[i] L ≘ K.ⓛV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & + ⬆*[↑i] V2 ≘ T2 & c = cV + 𝟘𝟙. #Rt #c #h #G #i elim i -i [ #L #T2 #H elim (cpg_inv_zero1 … H) -H * /3 width=1 by or3_intro0, conj/ /4 width=8 by drops_refl, ex4_4_intro, or3_intro2, or3_intro1/ @@ -64,10 +64,10 @@ qed-. lemma cpg_inv_atom1_drops: ∀Rt,c,h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ⬈[Rt, c, h] T2 → ∨∨ T2 = ⓪{I} ∧ c = 𝟘𝟘 | ∃∃s. T2 = ⋆(next h s) & I = Sort s & c = 𝟘𝟙 - | ∃∃cV,i,K,V,V2. ⬇*[i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & - ⬆*[⫯i] V2 ≡ T2 & I = LRef i & c = cV - | ∃∃cV,i,K,V,V2. ⬇*[i] L ≡ K.ⓛV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & - ⬆*[⫯i] V2 ≡ T2 & I = LRef i & c = cV + 𝟘𝟙. + | ∃∃cV,i,K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & + ⬆*[↑i] V2 ≘ T2 & I = LRef i & c = cV + | ∃∃cV,i,K,V,V2. ⬇*[i] L ≘ K.ⓛV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 & + ⬆*[↑i] V2 ≘ T2 & I = LRef i & c = cV + 𝟘𝟙. #Rt #c #h * #n #G #L #T2 #H [ elim (cpg_inv_sort1 … H) -H * /3 width=3 by or4_intro0, or4_intro1, ex3_intro, conj/ @@ -100,7 +100,7 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → elim (drops_inv_skip2 … HY) -HY #Z #L0 #HLK0 #HZ #H destruct elim (liftsb_inv_pair_sn … HZ) -HZ #W #HVW #H destruct elim (IH … HV2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -K -K0 -V #W2 #HVW2 #HW2 - elim (lifts_total W2 (𝐔❴⫯i2❵)) #U2 #HWU2 + elim (lifts_total W2 (𝐔❴↑i2❵)) #U2 #HWU2 lapply (lifts_trans … HVW2 … HWU2 ??) -HVW2 [3,6: |*: // ] #HVU2 lapply (lifts_conf … HVT2 … HVU2 f ?) -V2 [1,3: /2 width=3 by after_uni_succ_sn/ ] /4 width=8 by cpg_ell_drops, cpg_delta_drops, drops_inv_gen, ex2_intro/ @@ -118,7 +118,7 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → | #cT #T2 #HT12 #HXT2 #H1 #H2 #H3 destruct elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #U2 #HTU2 #HU12 lapply (lifts_trans … HXT2 … HTU2 ??) -T2 [3: |*: // ] #HXU2 - elim (lifts_split_trans … HXU2 f (𝐔❴⫯O❵)) [2: /2 width=1 by after_uni_one_dx/ ] + elim (lifts_split_trans … HXU2 f (𝐔❴↑O❵)) [2: /2 width=1 by after_uni_one_dx/ ] /3 width=5 by cpg_zeta, ex2_intro/ ] | * #V1 #T1 #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct @@ -141,7 +141,7 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] elim (lifts_total W2 (𝐔❴1❵)) #W20 #HW20 lapply (lifts_trans … HVW2 … HW20 ??) -HVW2 [3: |*: // ] #H - lapply (lifts_conf … HV20 … H (↑f) ?) -V2 /2 width=3 by after_uni_one_sn/ + lapply (lifts_conf … HV20 … H (⫯f) ?) -V2 /2 width=3 by after_uni_one_sn/ /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/ ] | elim (cpg_inv_cast1 … H2) -H2 * @@ -222,7 +222,7 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → elim (IH … HZ12 … HLK … HYZ1) -HZ12 // elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] lapply (lifts_trans … HVW2 … HW20 ??) -W2 [3: |*: // ] #H - elim (lifts_split_trans … H ? (↑f)) -H [ |*: /2 width=3 by after_uni_one_sn/ ] + elim (lifts_split_trans … H ? (⫯f)) -H [ |*: /2 width=3 by after_uni_one_sn/ ] /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/ ] | elim (cpg_inv_cast1 … H2) -H2 *