X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Funfold%2Fltpss_tpss.ma;h=c75119b66af51e71a2ce56cf1f1299e9120ff520;hb=db63f65c35efaa93d0a2cc00a194549e791975c9;hp=b8e425e631ab4908119467123776d588344edae6;hpb=55dc00c1c44cc21c7ae179cb9df03e7446002c46;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma index b8e425e63..c75119b66 100644 --- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma +++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_tpss.ma @@ -12,8 +12,8 @@ (* *) (**************************************************************************) -include "Basic-2/unfold/tpss_ltps.ma". -include "Basic-2/unfold/ltpss.ma". +include "Basic_2/unfold/tpss_ltps.ma". +include "Basic_2/unfold/ltpss.ma". (* PARTIAL UNFOLD ON LOCAL ENVIRONMENTS *************************************) @@ -24,28 +24,28 @@ lemma ltpss_tpss_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫* L0 → d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ≫* U2. #L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0 // #L #L0 #_ #HL0 #IHL #T2 #U2 #d2 #e2 #HTU2 #Hde1d2 -lapply (ltps_tpss_trans_ge … HL0 HTU2) -HL0 HTU2 /2/ +lapply (ltps_tpss_trans_ge … HL0 HTU2) -HL0 -HTU2 /2 width=1/ qed. lemma ltpss_tps_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫* L0 → ∀T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ≫ U2 → d1 + e1 ≤ d2 → L1 ⊢ T2 [d2, e2] ≫* U2. #L1 #L0 #d1 #e1 #HL10 #T2 #U2 #d2 #e2 #HTU2 #Hde1d2 -@(ltpss_tpss_trans_ge … HL10 … Hde1d2) /2/ (**) (* /3 width=6/ is too slow *) +@(ltpss_tpss_trans_ge … HL10 … Hde1d2) /2 width=1/ (**) (* /3 width=6/ is too slow *) qed. lemma ltpss_tpss_trans_eq: ∀L0,L1,d,e. L0 [d, e] ≫* L1 → ∀T2,U2. L1 ⊢ T2 [d, e] ≫* U2 → L0 ⊢ T2 [d, e] ≫* U2. #L0 #L1 #d #e #H @(ltpss_ind … H) -L1 -[ /2/ +[ /2 width=1/ | #L #L1 #_ #HL1 #IHL #T2 #U2 #HTU2 - lapply (ltps_tpss_trans_eq … HL1 HTU2) -HL1 HTU2 /2/ + lapply (ltps_tpss_trans_eq … HL1 HTU2) -HL1 -HTU2 /2 width=1/ ] qed. lemma ltpss_tps_trans_eq: ∀L0,L1,d,e. L0 [d, e] ≫* L1 → ∀T2,U2. L1 ⊢ T2 [d, e] ≫ U2 → L0 ⊢ T2 [d, e] ≫* U2. -/3/ qed. +/3 width=3/ qed. lemma ltpss_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 → L0 ⊢ T2 [d2, e2] ≫* U2 → L0 [d1, e1] ≫* L1 → @@ -53,7 +53,7 @@ lemma ltpss_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 → #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HTU2 #H @(ltpss_ind … H) -L1 [ // | -HTU2 #L #L1 #_ #HL1 #IHL - lapply (ltps_tpss_conf_ge … HL1 IHL) -HL1 IHL // + lapply (ltps_tpss_conf_ge … HL1 IHL) -HL1 -IHL // ] qed. @@ -61,45 +61,45 @@ lemma ltpss_tps_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2. d1 + e1 ≤ d2 → L0 ⊢ T2 [d2, e2] ≫ U2 → L0 [d1, e1] ≫* L1 → L1 ⊢ T2 [d2, e2] ≫* U2. #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HTU2 #HL01 -@(ltpss_tpss_conf_ge … Hde1d2 … HL01) /2/ (**) (* /3 width=6/ is too slow *) +@(ltpss_tpss_conf_ge … Hde1d2 … HL01) /2 width=1/ (**) (* /3 width=6/ is too slow *) qed. lemma ltpss_tpss_conf_eq: ∀L0,L1,T2,U2,d,e. L0 ⊢ T2 [d, e] ≫* U2 → L0 [d, e] ≫* L1 → ∃∃T. L1 ⊢ T2 [d, e] ≫* T & L1 ⊢ U2 [d, e] ≫* T. #L0 #L1 #T2 #U2 #d #e #HTU2 #H @(ltpss_ind … H) -L1 -[ /2/ +[ /2 width=3/ | -HTU2 #L #L1 #_ #HL1 * #W2 #HTW2 #HUW2 elim (ltps_tpss_conf … HL1 HTW2) -HTW2 #T #HT2 #HW2T - elim (ltps_tpss_conf … HL1 HUW2) -HL1 HUW2 #U #HU2 #HW2U - elim (tpss_conf_eq … HW2T … HW2U) -HW2T HW2U #V #HTV #HUV - lapply (tpss_trans_eq … HT2 … HTV) -T; - lapply (tpss_trans_eq … HU2 … HUV) -U /2/ + elim (ltps_tpss_conf … HL1 HUW2) -HL1 -HUW2 #U #HU2 #HW2U + elim (tpss_conf_eq … HW2T … HW2U) -HW2T -HW2U #V #HTV #HUV + lapply (tpss_trans_eq … HT2 … HTV) -T + lapply (tpss_trans_eq … HU2 … HUV) -U /2 width=3/ ] qed. lemma ltpss_tps_conf_eq: ∀L0,L1,T2,U2,d,e. L0 ⊢ T2 [d, e] ≫ U2 → L0 [d, e] ≫* L1 → ∃∃T. L1 ⊢ T2 [d, e] ≫* T & L1 ⊢ U2 [d, e] ≫* T. -/3/ qed. +/3 width=3/ qed. lemma ltpss_tpss_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫* T2 → ∀L2,ds,es. L1 [ds, es] ≫* L2 → ∃∃T. L2 ⊢ T1 [d, e] ≫* T & L1 ⊢ T2 [ds, es] ≫* T. #L1 #T1 #T2 #d #e #HT12 #L2 #ds #es #H @(ltpss_ind … H) -L2 -[ /3/ +[ /3 width=3/ | #L #L2 #HL1 #HL2 * #T #HT1 #HT2 elim (ltps_tpss_conf … HL2 HT1) -HT1 #T0 #HT10 #HT0 - lapply (ltps_tpss_trans_eq … HL2 … HT0) -HL2 HT0 #HT0 - lapply (ltpss_tpss_trans_eq … HL1 … HT0) -HL1 HT0 #HT0 - lapply (tpss_trans_eq … HT2 … HT0) -T /2/ + lapply (ltps_tpss_trans_eq … HL2 … HT0) -HL2 -HT0 #HT0 + lapply (ltpss_tpss_trans_eq … HL1 … HT0) -HL1 -HT0 #HT0 + lapply (tpss_trans_eq … HT2 … HT0) -T /2 width=3/ ] qed. lemma ltpss_tps_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫ T2 → ∀L2,ds,es. L1 [ds, es] ≫* L2 → ∃∃T. L2 ⊢ T1 [d, e] ≫* T & L1 ⊢ T2 [ds, es] ≫* T. -/3/ qed. +/3 width=1/ qed. (* Advanced properties ******************************************************) @@ -107,10 +107,10 @@ lemma ltpss_tps2: ∀L1,L2,I,e. L1 [0, e] ≫* L2 → ∀V1,V2. L2 ⊢ V1 [0, e] ≫ V2 → L1. 𝕓{I} V1 [0, e + 1] ≫* L2. 𝕓{I} V2. #L1 #L2 #I #e #H @(ltpss_ind … H) -L2 -[ /3/ +[ /3 width=1/ | #L #L2 #_ #HL2 #IHL #V1 #V2 #HV12 elim (ltps_tps_trans … HV12 … HL2) -HV12 #V #HV1 #HV2 - lapply (IHL … HV1) -IHL HV1 #HL1 + lapply (IHL … HV1) -IHL -HV1 #HL1 @step /2 width=5/ (**) (* /3 width=5/ is too slow *) ] qed. @@ -119,17 +119,17 @@ lemma ltpss_tps2_lt: ∀L1,L2,I,V1,V2,e. L1 [0, e - 1] ≫* L2 → L2 ⊢ V1 [0, e - 1] ≫ V2 → 0 < e → L1. 𝕓{I} V1 [0, e] ≫* L2. 𝕓{I} V2. #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He ->(plus_minus_m_m e 1) /2/ +>(plus_minus_m_m e 1) // /2 width=1/ qed. lemma ltpss_tps1: ∀L1,L2,I,d,e. L1 [d, e] ≫* L2 → ∀V1,V2. L2 ⊢ V1 [d, e] ≫ V2 → L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2. #L1 #L2 #I #d #e #H @(ltpss_ind … H) -L2 -[ /3/ +[ /3 width=1/ | #L #L2 #_ #HL2 #IHL #V1 #V2 #HV12 elim (ltps_tps_trans … HV12 … HL2) -HV12 #V #HV1 #HV2 - lapply (IHL … HV1) -IHL HV1 #HL1 + lapply (IHL … HV1) -IHL -HV1 #HL1 @step /2 width=5/ (**) (* /3 width=5/ is too slow *) ] qed. @@ -138,22 +138,22 @@ lemma ltpss_tps1_lt: ∀L1,L2,I,V1,V2,d,e. L1 [d - 1, e] ≫* L2 → L2 ⊢ V1 [d - 1, e] ≫ V2 → 0 < d → L1. 𝕓{I} V1 [d, e] ≫* L2. 𝕓{I} V2. #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #Hd ->(plus_minus_m_m d 1) /2/ +>(plus_minus_m_m d 1) // /2 width=1/ qed. (* Advanced forward lemmas **************************************************) -lemma ltpss_fwd_tpsa21: ∀e,K1,I,V1,L2. 0 < e → K1. 𝕓{I} V1 [0, e] ≫* L2 → +lemma ltpss_fwd_tpss21: ∀e,K1,I,V1,L2. 0 < e → K1. 𝕓{I} V1 [0, e] ≫* L2 → ∃∃K2,V2. K1 [0, e - 1] ≫* K2 & K1 ⊢ V1 [0, e - 1] ≫* V2 & L2 = K2. 𝕓{I} V2. #e #K1 #I #V1 #L2 #He #H @(ltpss_ind … H) -L2 [ /2 width=5/ -| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct -L; +| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct elim (ltps_inv_tps21 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H lapply (ltps_tps_trans_eq … HV2 … HK2) -HV2 #HV2 lapply (ltpss_tpss_trans_eq … HK1 … HV2) -HV2 #HV2 /3 width=5/ ] -qed. +qed-. lemma ltpss_fwd_tpss11: ∀d,e,I,K1,V1,L2. 0 < d → K1. 𝕓{I} V1 [d, e] ≫* L2 → ∃∃K2,V2. K1 [d - 1, e] ≫* K2 & @@ -161,9 +161,9 @@ lemma ltpss_fwd_tpss11: ∀d,e,I,K1,V1,L2. 0 < d → K1. 𝕓{I} V1 [d, e] ≫* L2 = K2. 𝕓{I} V2. #d #e #K1 #I #V1 #L2 #Hd #H @(ltpss_ind … H) -L2 [ /2 width=5/ -| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct -L; +| #L #L2 #_ #HL2 * #K #V #HK1 #HV1 #H destruct elim (ltps_inv_tps11 … HL2 ?) -HL2 // #K2 #V2 #HK2 #HV2 #H lapply (ltps_tps_trans_eq … HV2 … HK2) -HV2 #HV2 lapply (ltpss_tpss_trans_eq … HK1 … HV2) -HV2 #HV2 /3 width=5/ ] -qed. +qed-.