X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpg_drops.ma;h=6bfc84c4e1088071ca8d7c7eea4a1eb14e546aae;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=8a5f96f91e5329bddf185fb339f80e6b273b4ba7;hpb=f129bbbfda0e65a5f92ec086246f6e288376d4f9;p=helm.git 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 8a5f96f91..6bfc84c4e 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 @@ -12,43 +12,44 @@ (* *) (**************************************************************************) -include "basic_2/relocation/drops_drops.ma". -include "basic_2/s_computation/fqup_weight.ma". -include "basic_2/s_computation/fqup_drops.ma". +include "ground_2/xoa/ex_5_5.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". (* 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. (* Advanced inversion lemmas ************************************************) -lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2 → +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/ @@ -61,13 +62,13 @@ lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2 ] 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. +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 = ⋆(⫯[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. #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 +101,7 @@ 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/ @@ -115,10 +116,9 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → elim (IH … HV12 … HLK … HVW1) -HV12 // elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] /3 width=5 by cpg_bind, lifts_bind, ex2_intro/ - | #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/ ] + | #cT #T2 #HT21 #HTX2 #H1 #H2 #H3 destruct + elim (lifts_trans4_one … HT21 … HTU1) -HTU1 #U2 #HTU2 #HU21 + elim (IH … HTX2 … HLK … HTU2) [| /3 width=1 by fqup_zeta/ ] -K -V1 -T1 -T2 /3 width=5 by cpg_zeta, ex2_intro/ ] | * #V1 #T1 #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct @@ -139,7 +139,7 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 // #W2 #HVW2 #HW12 elim (IH … HY12 … HLK … HYZ1) -HY12 // elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] - elim (lifts_total W2 (𝐔❴1❵)) #W20 #HW20 + 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/ /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/ @@ -179,7 +179,7 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → [ #H1 #H2 destruct /3 width=3 by cpg_refl, ex2_intro/ ] #cW #L0 #W #W2 #HL0 #HW2 #HWU2 #H destruct elim (lifts_inv_lref2 … H1) -H1 #i1 #Hf #H destruct - lapply (drops_split_div … HLK (𝐔❴i1❵) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0 + lapply (drops_split_div … HLK (𝐔❨i1❩) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0 lapply (drops_conf … HL0 … HLY0 ??) -HLY0 [3,6: |*: /2 width=6 by after_uni_dx/ ] #HLY0 lapply (drops_tls_at … Hf … HLY0) -HLY0 #HLY0 elim (drops_inv_skip1 … HLY0) -HLY0 #Z #K0 #HLK0 #HZ #H destruct @@ -199,9 +199,10 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → elim (IH … HW12 … HLK … HVW1) -HW12 // elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] /3 width=5 by cpg_bind, lifts_bind, ex2_intro/ - | #cU #U2 #HU12 #HXU2 #H1 #H2 #H3 destruct - elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #T2 #HTU2 #HT12 - elim (lifts_div4_one … HTU2 … HXU2) -U2 /3 width=5 by cpg_zeta, ex2_intro/ + | #cU #U2 #HU21 #HUX2 #H1 #H2 #H3 destruct + elim (lifts_div4_one … HTU1 … HU21) -HTU1 #T2 #HT21 #HTU2 + elim (IH … HUX2 … HLK … HTU2) [| /3 width=1 by fqup_zeta/ ] -L -W1 -U1 -U2 + /3 width=5 by cpg_zeta, ex2_intro/ ] | * #W1 #U1 #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #HVW1 #HTU1 #H destruct