X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Funfold%2Ftpss_lift.ma;h=a68f86e32bfafd063900f7e0ad66ec63fe546d90;hb=eae50cc815292d335df1c488a00b39ef98fa5870;hp=b5244430024b5adb5022007d39b43f017610d177;hpb=636c25914e83819c2f529edc891a7eb899499a97;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/tpss_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/tpss_lift.ma index b52444300..a68f86e32 100644 --- a/matita/matita/contribs/lambda_delta/basic_2/unfold/tpss_lift.ma +++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/tpss_lift.ma @@ -21,8 +21,8 @@ include "basic_2/unfold/tpss.ma". lemma tpss_subst: ∀L,K,V,U1,i,d,e. d ≤ i → i < d + e → - ⇩[0, i] L ≡ K. ⓓV → K ⊢ V [0, d + e - i - 1] ▶* U1 → - ∀U2. ⇧[0, i + 1] U1 ≡ U2 → L ⊢ #i [d, e] ▶* U2. + ⇩[0, i] L ≡ K. ⓓV → K ⊢ V ▶* [0, d + e - i - 1] U1 → + ∀U2. ⇧[0, i + 1] U1 ≡ U2 → L ⊢ #i ▶* [d, e] U2. #L #K #V #U1 #i #d #e #Hdi #Hide #HLK #H @(tpss_ind … H) -U1 [ /3 width=4/ | #U #U1 #_ #HU1 #IHU #U2 #HU12 @@ -36,11 +36,11 @@ qed. (* Advanced inverion lemmas *************************************************) -lemma tpss_inv_atom1: ∀L,T2,I,d,e. L ⊢ ⓪{I} [d, e] ▶* T2 → +lemma tpss_inv_atom1: ∀L,T2,I,d,e. L ⊢ ⓪{I} ▶* [d, e] T2 → T2 = ⓪{I} ∨ ∃∃K,V1,V2,i. d ≤ i & i < d + e & ⇩[O, i] L ≡ K. ⓓV1 & - K ⊢ V1 [0, d + e - i - 1] ▶* V2 & + K ⊢ V1 ▶* [0, d + e - i - 1] V2 & ⇧[O, i + 1] V2 ≡ T2 & I = LRef i. #L #T2 #I #d #e #H @(tpss_ind … H) -T2 @@ -56,25 +56,25 @@ lemma tpss_inv_atom1: ∀L,T2,I,d,e. L ⊢ ⓪{I} [d, e] ▶* T2 → ] qed-. -lemma tpss_inv_lref1: ∀L,T2,i,d,e. L ⊢ #i [d, e] ▶* T2 → +lemma tpss_inv_lref1: ∀L,T2,i,d,e. L ⊢ #i ▶* [d, e] T2 → T2 = #i ∨ ∃∃K,V1,V2. d ≤ i & i < d + e & ⇩[O, i] L ≡ K. ⓓV1 & - K ⊢ V1 [0, d + e - i - 1] ▶* V2 & + K ⊢ V1 ▶* [0, d + e - i - 1] V2 & ⇧[O, i + 1] V2 ≡ T2. #L #T2 #i #d #e #H elim (tpss_inv_atom1 … H) -H /2 width=1/ * #K #V1 #V2 #j #Hdj #Hjde #HLK #HV12 #HVT2 #H destruct /3 width=6/ qed-. -lemma tpss_inv_S2: ∀L,T1,T2,d,e. L ⊢ T1 [d, e + 1] ▶* T2 → - ∀K,V. ⇩[0, d] L ≡ K. ⓛV → L ⊢ T1 [d + 1, e] ▶* T2. +lemma tpss_inv_S2: ∀L,T1,T2,d,e. L ⊢ T1 ▶* [d, e + 1] T2 → + ∀K,V. ⇩[0, d] L ≡ K. ⓛV → L ⊢ T1 ▶* [d + 1, e] T2. #L #T1 #T2 #d #e #H #K #V #HLK @(tpss_ind … H) -T2 // #T #T2 #_ #HT2 #IHT lapply (tps_inv_S2 … HT2 … HLK) -HT2 -HLK /2 width=3/ qed-. -lemma tpss_inv_refl_SO2: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ▶* T2 → +lemma tpss_inv_refl_SO2: ∀L,T1,T2,d. L ⊢ T1 ▶* [d, 1] T2 → ∀K,V. ⇩[0, d] L ≡ K. ⓛV → T1 = T2. #L #T1 #T2 #d #H #K #V #HLK @(tpss_ind … H) -T2 // #T #T2 #_ #HT2 #IHT <(tps_inv_refl_SO2 … HT2 … HLK) // @@ -82,10 +82,10 @@ qed-. (* Relocation properties ****************************************************) -lemma tpss_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶* T2 → +lemma tpss_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 ▶* [dt, et] T2 → ∀L,U1,d,e. dt + et ≤ d → ⇩[d, e] L ≡ K → ⇧[d, e] T1 ≡ U1 → ∀U2. ⇧[d, e] T2 ≡ U2 → - L ⊢ U1 [dt, et] ▶* U2. + L ⊢ U1 ▶* [dt, et] U2. #K #T1 #T2 #dt #et #H #L #U1 #d #e #Hdetd #HLK #HTU1 @(tpss_ind … H) -T2 [ #U2 #H >(lift_mono … HTU1 … H) -H // | -HTU1 #T #T2 #_ #HT2 #IHT #U2 #HTU2 @@ -95,10 +95,10 @@ lemma tpss_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶* T2 → ] qed. -lemma tpss_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶* T2 → +lemma tpss_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 ▶* [dt, et] T2 → ∀L,U1,d,e. dt ≤ d → d ≤ dt + et → ⇩[d, e] L ≡ K → ⇧[d, e] T1 ≡ U1 → - ∀U2. ⇧[d, e] T2 ≡ U2 → L ⊢ U1 [dt, et + e] ▶* U2. + ∀U2. ⇧[d, e] T2 ≡ U2 → L ⊢ U1 ▶* [dt, et + e] U2. #K #T1 #T2 #dt #et #H #L #U1 #d #e #Hdtd #Hddet #HLK #HTU1 @(tpss_ind … H) -T2 [ #U2 #H >(lift_mono … HTU1 … H) -H // | -HTU1 #T #T2 #_ #HT2 #IHT #U2 #HTU2 @@ -108,10 +108,10 @@ lemma tpss_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶* T2 → ] qed. -lemma tpss_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶* T2 → +lemma tpss_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 ▶* [dt, et] T2 → ∀L,U1,d,e. d ≤ dt → ⇩[d, e] L ≡ K → ⇧[d, e] T1 ≡ U1 → ∀U2. ⇧[d, e] T2 ≡ U2 → - L ⊢ U1 [dt + e, et] ▶* U2. + L ⊢ U1 ▶* [dt + e, et] U2. #K #T1 #T2 #dt #et #H #L #U1 #d #e #Hddt #HLK #HTU1 @(tpss_ind … H) -T2 [ #U2 #H >(lift_mono … HTU1 … H) -H // | -HTU1 #T #T2 #_ #HT2 #IHT #U2 #HTU2 @@ -121,10 +121,10 @@ lemma tpss_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ▶* T2 → ] qed. -lemma tpss_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → +lemma tpss_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 #K #d #e #HLK #T1 #HTU1 #Hdetd @(tpss_ind … H) -U2 [ /2 width=3/ | -HTU1 #U #U2 #_ #HU2 * #T #HT1 #HTU @@ -132,10 +132,10 @@ lemma tpss_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → ] qed. -lemma tpss_inv_lift1_be: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → +lemma tpss_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 #K #d #e #HLK #T1 #HTU1 #Hdtd #Hdedet @(tpss_ind … H) -U2 [ /2 width=3/ | -HTU1 #U #U2 #_ #HU2 * #T #HT1 #HTU @@ -143,10 +143,10 @@ lemma tpss_inv_lift1_be: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → ] qed. -lemma tpss_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → +lemma tpss_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 #K #d #e #HLK #T1 #HTU1 #Hdedt @(tpss_ind … H) -U2 [ /2 width=3/ | -HTU1 #U #U2 #_ #HU2 * #T #HT1 #HTU @@ -155,16 +155,16 @@ lemma tpss_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → qed. lemma tpss_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 #T1 #HTU1 @(tpss_ind … H) -U2 // #U #U2 #_ #HU2 #IHU destruct <(tps_inv_lift1_eq … HU2 … HTU1) -HU2 -HTU1 // qed. -lemma tpss_inv_lift1_ge_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → +lemma tpss_inv_lift1_ge_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 & + ∃∃T2. K ⊢ T1 ▶* [d, dt + et - (d + e)] T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #H #K #d #e #HLK #T1 #HTU1 #Hddt #Hdtde #Hdedet @(tpss_ind … H) -U2 [ /2 width=3/ @@ -173,10 +173,10 @@ lemma tpss_inv_lift1_ge_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → ] qed. -lemma tpss_inv_lift1_be_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → +lemma tpss_inv_lift1_be_up: ∀L,U1,U2,dt,et. L ⊢ U1 ▶* [dt, et] U2 → ∀K,d,e. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 → dt ≤ d → dt + et ≤ d + e → - ∃∃T2. K ⊢ T1 [dt, d - dt] ▶* T2 & ⇧[d, e] T2 ≡ U2. + ∃∃T2. K ⊢ T1 ▶* [dt, d - dt] T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #H #K #d #e #HLK #T1 #HTU1 #Hdtd #Hdetde @(tpss_ind … H) -U2 [ /2 width=3/ | -HTU1 #U #U2 #_ #HU2 * #T #HT1 #HTU @@ -184,10 +184,10 @@ lemma tpss_inv_lift1_be_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → ] qed. -lemma tpss_inv_lift1_le_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 → +lemma tpss_inv_lift1_le_up: ∀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 ≤ dt + et → dt + et ≤ d + e → - ∃∃T2. K ⊢ T1 [dt, d - dt] ▶* T2 & ⇧[d, e] T2 ≡ U2. + ∃∃T2. K ⊢ T1 ▶* [dt, d - dt] T2 & ⇧[d, e] T2 ≡ U2. #L #U1 #U2 #dt #et #H #K #d #e #HLK #T1 #HTU1 #Hdtd #Hddet #Hdetde @(tpss_ind … H) -U2 [ /2 width=3/ | -HTU1 #U #U2 #_ #HU2 * #T #HT1 #HTU