X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Ftps_lift.ma;fp=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Ftps_lift.ma;h=78c324e4661382962b3df5076dc919dc3177f1de;hb=39e80f80b26e18cf78f805e814ba2f2e8400c1f1;hp=3b1453c37e951c657990f90e38d260ff9df131f2;hpb=de392360825733c1c865d748f7711f34bfc027f3;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma index 3b1453c37..78c324e46 100644 --- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma +++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma @@ -19,8 +19,8 @@ include "Basic_2/substitution/tps.ma". (* Advanced inversion lemmas ************************************************) -fact tps_inv_refl_SO2_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → e = 1 → - ∀K,V. ⇓[0, d] L ≡ K. 𝕓{Abst} V → T1 = T2. +fact tps_inv_refl_SO2_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶ T2 → e = 1 → + ∀K,V. ⇩[0, d] L ≡ K. 𝕓{Abst} V → T1 = T2. #L #T1 #T2 #d #e #H elim H -L -T1 -T2 -d -e [ // | #L #K0 #V0 #W #i #d #e #Hdi #Hide #HLK0 #_ #H destruct @@ -33,18 +33,18 @@ fact tps_inv_refl_SO2_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → e = 1 → ] qed. -lemma tps_inv_refl_SO2: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ≫ T2 → - ∀K,V. ⇓[0, d] L ≡ K. 𝕓{Abst} V → T1 = T2. +lemma tps_inv_refl_SO2: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ▶ T2 → + ∀K,V. ⇩[0, d] L ≡ K. 𝕓{Abst} V → T1 = T2. /2 width=8/ qed-. (* Relocation properties ****************************************************) (* Basic_1: was: subst1_lift_lt *) -lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → - ∀L,U1,U2,d,e. ⇓[d, e] L ≡ K → - ⇑[d, e] T1 ≡ U1 → ⇑[d, e] T2 ≡ U2 → +lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶ T2 → + ∀L,U1,U2,d,e. ⇩[d, e] L ≡ K → + ⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 → dt + et ≤ d → - L ⊢ U1 [dt, et] ≫ U2. + L ⊢ U1 [dt, et] ▶ U2. #K #T1 #T2 #dt #et #H elim H -K -T1 -T2 -dt -et [ #K #I #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ >(lift_mono … H1 … H2) -H1 -H2 // @@ -65,11 +65,11 @@ lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → ] qed. -lemma tps_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → - ∀L,U1,U2,d,e. ⇓[d, e] L ≡ K → - ⇑[d, e] T1 ≡ U1 → ⇑[d, e] T2 ≡ U2 → +lemma tps_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶ T2 → + ∀L,U1,U2,d,e. ⇩[d, e] L ≡ K → + ⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 → dt ≤ d → d ≤ dt + et → - L ⊢ U1 [dt, et + e] ≫ U2. + L ⊢ U1 [dt, et + e] ▶ U2. #K #T1 #T2 #dt #et #H elim H -K -T1 -T2 -dt -et [ #K #I #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ #_ >(lift_mono … H1 … H2) -H1 -H2 // @@ -98,11 +98,11 @@ lemma tps_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → qed. (* Basic_1: was: subst1_lift_ge *) -lemma tps_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → - ∀L,U1,U2,d,e. ⇓[d, e] L ≡ K → - ⇑[d, e] T1 ≡ U1 → ⇑[d, e] T2 ≡ U2 → +lemma tps_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶ T2 → + ∀L,U1,U2,d,e. ⇩[d, e] L ≡ K → + ⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 → d ≤ dt → - L ⊢ U1 [dt + e, et] ≫ U2. + L ⊢ U1 [dt + e, et] ▶ U2. #K #T1 #T2 #dt #et #H elim H -K -T1 -T2 -dt -et [ #K #I #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ >(lift_mono … H1 … H2) -H1 -H2 // @@ -122,10 +122,10 @@ lemma tps_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → qed. (* Basic_1: was: subst1_gen_lift_lt *) -lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → - ∀K,d,e. ⇓[d, e] L ≡ K → ∀T1. ⇑[d, e] T1 ≡ U1 → +lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶ U2 → + ∀K,d,e. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 → dt + et ≤ d → - ∃∃T2. K ⊢ T1 [dt, et] ≫ T2 & ⇑[d, e] T2 ≡ U2. + ∃∃T2. K ⊢ T1 [dt, et] ▶ T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #H elim H -L -U1 -U2 -dt -et [ #L * #i #dt #et #K #d #e #_ #T1 #H #_ [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/ @@ -149,10 +149,10 @@ lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → ] qed. -lemma tps_inv_lift1_be: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → - ∀K,d,e. ⇓[d, e] L ≡ K → ∀T1. ⇑[d, e] T1 ≡ U1 → +lemma tps_inv_lift1_be: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶ U2 → + ∀K,d,e. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 → dt ≤ d → d + e ≤ dt + et → - ∃∃T2. K ⊢ T1 [dt, et - e] ≫ T2 & ⇑[d, e] T2 ≡ U2. + ∃∃T2. K ⊢ T1 [dt, et - e] ▶ T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #H elim H -L -U1 -U2 -dt -et [ #L * #i #dt #et #K #d #e #_ #T1 #H #_ [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/ @@ -187,10 +187,10 @@ lemma tps_inv_lift1_be: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → qed. (* Basic_1: was: subst1_gen_lift_ge *) -lemma tps_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → - ∀K,d,e. ⇓[d, e] L ≡ K → ∀T1. ⇑[d, e] T1 ≡ U1 → +lemma tps_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶ U2 → + ∀K,d,e. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 → d + e ≤ dt → - ∃∃T2. K ⊢ T1 [dt - e, et] ≫ T2 & ⇑[d, e] T2 ≡ U2. + ∃∃T2. K ⊢ T1 [dt - e, et] ▶ T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #H elim H -L -U1 -U2 -dt -et [ #L * #i #dt #et #K #d #e #_ #T1 #H #_ [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/ @@ -221,7 +221,7 @@ qed. (* Basic_1: was: subst1_gen_lift_eq *) lemma tps_inv_lift1_eq: ∀L,U1,U2,d,e. - L ⊢ U1 [d, e] ≫ U2 → ∀T1. ⇑[d, e] T1 ≡ U1 → U1 = U2. + L ⊢ U1 [d, e] ▶ U2 → ∀T1. ⇧[d, e] T1 ≡ U1 → U1 = U2. #L #U1 #U2 #d #e #H elim H -L -U1 -U2 -d -e [ // | #L #K #V #W #i #d #e #Hdi #Hide #_ #_ #T1 #H @@ -253,10 +253,10 @@ qed. (le d i) -> (lt i (plus d h)) -> (EX u1 | t1 = (lift (minus (plus d h) (S i)) (S i) u1)). *) -lemma tps_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → - ∀K,d,e. ⇓[d, e] L ≡ K → ∀T1. ⇑[d, e] T1 ≡ U1 → +lemma tps_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶ U2 → + ∀K,d,e. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 → d ≤ dt → dt ≤ d + e → d + e ≤ dt + et → - ∃∃T2. K ⊢ T1 [d, dt + et - (d + e)] ≫ T2 & ⇑[d, e] T2 ≡ U2. + ∃∃T2. K ⊢ T1 [d, dt + et - (d + e)] ▶ T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #HU12 #K #d #e #HLK #T1 #HTU1 #Hddt #Hdtde #Hdedet elim (tps_split_up … HU12 (d + e) ? ?) -HU12 // -Hdedet #U #HU1 #HU2 lapply (tps_weak … HU1 d e ? ?) -HU1 // [ >commutative_plus /2 width=1/ ] -Hddt -Hdtde #HU1 @@ -264,10 +264,10 @@ lapply (tps_inv_lift1_eq … HU1 … HTU1) -HU1 #HU1 destruct elim (tps_inv_lift1_ge … HU2 … HLK … HTU1 ?) -U -L //