From eaa8cd77b9060af69694327d609b18473b075f4d Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Mon, 22 Aug 2011 12:34:34 +0000 Subject: [PATCH] we now use non-telescopic substitution in parallel reduction, rather than the telescopic one. This choice weakens the step of context-sensitive reduction a bit while maintaining the expected properties --- .../lambda-delta/Basic-2/reduction/cpr.ma | 10 ++-- .../lambda-delta/Basic-2/reduction/lcpr.ma | 6 +-- .../lambda-delta/Basic-2/substitution/tps.ma | 48 ++++++++----------- .../Basic-2/substitution/tps_lift.ma | 48 +++++++++---------- .../Basic-2/substitution/tps_split.ma | 20 +++----- .../Basic-2/substitution/tps_tps.ma | 32 +++++-------- 6 files changed, 67 insertions(+), 97 deletions(-) diff --git a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma index 21169192c..f41999e45 100644 --- a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma +++ b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma @@ -29,7 +29,7 @@ lemma cpr_pr: ∀T1,T2. T1 ⇒ T2 → ∀L. L ⊢ T1 ⇒ T2. /2/ qed. lemma cpr_tps: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → L ⊢ T1 ⇒ T2. -/3 width=5/ qed. +/3 width=5/ qed. lemma cpr_refl: ∀L,T. L ⊢ T ⇒ T. /2/ qed. @@ -40,11 +40,9 @@ lemma cpr_flat: ∀I,L,V1,V2,T1,T2. #I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 * /3 width=5/ qed. -lemma cpr_delta: ∀L,K,V1,V2,V,i. - ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫ V2 → - ↑[0, i + 1] V2 ≡ V → L ⊢ #i ⇒ V. -#L #K #V1 #V2 #V #i #HLK #HV12 #HV2 -@ex2_1_intro [2: // | skip ] /3 width=8/ (**) (* /4/ is too slow *) +lemma cpr_delta: ∀L,K,V,W,i. + ↓[0, i] L ≡ K. 𝕓{Abbr} V → ↑[0, i + 1] V ≡ W → L ⊢ #i ⇒ W. +/3/ qed. lemma cpr_cast: ∀L,V,T1,T2. diff --git a/matita/matita/contribs/lambda-delta/Basic-2/reduction/lcpr.ma b/matita/matita/contribs/lambda-delta/Basic-2/reduction/lcpr.ma index 1b19df78f..3098a2456 100644 --- a/matita/matita/contribs/lambda-delta/Basic-2/reduction/lcpr.ma +++ b/matita/matita/contribs/lambda-delta/Basic-2/reduction/lcpr.ma @@ -19,7 +19,7 @@ include "Basic-2/reduction/cpr.ma". inductive lcpr: lenv → lenv → Prop ≝ | lcpr_sort: lcpr (⋆) (⋆) | lcpr_item: ∀K1,K2,I,V1,V2. - lcpr K1 K2 → K1 ⊢ V1 ⇒ V2 → lcpr (K1. 𝕓{I} V1) (K2. 𝕓{I} V2) (*𝕓*) + lcpr K1 K2 → K2 ⊢ V1 ⇒ V2 → lcpr (K1. 𝕓{I} V1) (K2. 𝕓{I} V2) (*𝕓*) . interpretation @@ -29,7 +29,7 @@ interpretation (* Basic inversion lemmas ***************************************************) lemma lcpr_inv_item1_aux: ∀L1,L2. L1 ⊢ ⇒ L2 → ∀K1,I,V1. L1 = K1. 𝕓{I} V1 → - ∃∃K2,V2. K1 ⊢ ⇒ K2 & K1 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2. + ∃∃K2,V2. K1 ⊢ ⇒ K2 & K2 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2. #L1 #L2 * -L1 L2 [ #K1 #I #V1 #H destruct | #K1 #K2 #I #V1 #V2 #HK12 #HV12 #L #J #W #H destruct - K1 I V1 /2 width=5/ @@ -37,5 +37,5 @@ lemma lcpr_inv_item1_aux: ∀L1,L2. L1 ⊢ ⇒ L2 → ∀K1,I,V1. L1 = K1. 𝕓{ qed. lemma lcpr_inv_item1: ∀K1,I,V1,L2. K1. 𝕓{I} V1 ⊢ ⇒ L2 → - ∃∃K2,V2. K1 ⊢ ⇒ K2 & K1 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2. + ∃∃K2,V2. K1 ⊢ ⇒ K2 & K2 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2. /2/ qed. diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps.ma index d2c9e636b..bc82e4e6d 100644 --- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps.ma +++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps.ma @@ -14,15 +14,13 @@ include "Basic-2/substitution/drop.ma". -(* PARTIAL SUBSTITUTION ON TERMS ********************************************) +(* PARALLEL SUBSTITUTION ON TERMS *******************************************) inductive tps: lenv → term → nat → nat → term → Prop ≝ | tps_sort : ∀L,k,d,e. tps L (⋆k) d e (⋆k) | tps_lref : ∀L,i,d,e. tps L (#i) d e (#i) -| tps_subst: ∀L,K,V,U1,U2,i,d,e. - d ≤ i → i < d + e → - ↓[0, i] L ≡ K. 𝕓{Abbr} V → tps K V 0 (d + e - i - 1) U1 → - ↑[0, i + 1] U1 ≡ U2 → tps L (#i) d e U2 +| tps_subst: ∀L,K,V,W,i,d,e. d ≤ i → i < d + e → + ↓[0, i] L ≡ K. 𝕓{Abbr} V → ↑[0, i + 1] V ≡ W → tps L (#i) d e W | tps_bind : ∀L,I,V1,V2,T1,T2,d,e. tps L V1 d e V2 → tps (L. 𝕓{I} V1) T1 (d + 1) e T2 → tps L (𝕓{I} V1. T1) d e (𝕓{I} V2. T2) @@ -31,7 +29,7 @@ inductive tps: lenv → term → nat → nat → term → Prop ≝ tps L (𝕗{I} V1. T1) d e (𝕗{I} V2. T2) . -interpretation "partial telescopic substritution" +interpretation "parallel substritution (term)" 'PSubst L T1 d e T2 = (tps L T1 d e T2). (* Basic properties *********************************************************) @@ -41,9 +39,8 @@ lemma tps_leq_repl: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≫ T2 → #L1 #T1 #T2 #d #e #H elim H -H L1 T1 T2 d e [ // | // -| #L1 #K1 #V #V1 #V2 #i #d #e #Hdi #Hide #HLK1 #_ #HV12 #IHV12 #L2 #HL12 - elim (drop_leq_drop1 … HL12 … HLK1 ? ?) -HL12 HLK1 // #K2 #HK12 #HLK2 - @tps_subst [4,5,6,8: // |1,2,3: skip | /2/ ] (**) (* /3 width=6/ is too slow *) +| #L1 #K1 #V #W #i #d #e #Hdi #Hide #HLK1 #HVW #L2 #HL12 + elim (drop_leq_drop1 … HL12 … HLK1 ? ?) -HL12 HLK1 // /2/ | /4/ | /3/ ] @@ -60,10 +57,9 @@ lemma tps_weak: ∀L,T1,T2,d1,e1. L ⊢ T1 [d1, e1] ≫ T2 → #L #T1 #T #d1 #e1 #H elim H -L T1 T d1 e1 [ // | // -| #L #K #V #V1 #V2 #i #d1 #e1 #Hid1 #Hide1 #HLK #_ #HV12 #IHV12 #d2 #e2 #Hd12 #Hde12 +| #L #K #V #W #i #d1 #e1 #Hid1 #Hide1 #HLK #HVW #d2 #e2 #Hd12 #Hde12 lapply (transitive_le … Hd12 … Hid1) -Hd12 Hid1 #Hid2 - lapply (lt_to_le_to_lt … Hide1 … Hde12) -Hide1 #Hide2 - @tps_subst [4,5,6,8: // |1,2,3: skip | @IHV12 /2/ ] (**) (* /4 width=6/ is too slow *) + lapply (lt_to_le_to_lt … Hide1 … Hde12) -Hide1 /2/ | /4/ | /4/ ] @@ -74,12 +70,10 @@ lemma tps_weak_top: ∀L,T1,T2,d,e. #L #T1 #T #d #e #H elim H -L T1 T d e [ // | // -| #L #K #V #V1 #V2 #i #d #e #Hdi #_ #HLK #_ #HV12 #IHV12 +| #L #K #V #W #i #d #e #Hdi #_ #HLK #HVW lapply (drop_fwd_drop2_length … HLK) #Hi lapply (le_to_lt_to_lt … Hdi Hi) #Hd - lapply (plus_minus_m_m_comm (|L|) d ?) [ /2/ ] -Hd #Hd - lapply (drop_fwd_O1_length … HLK) normalize #HKL - lapply (tps_weak … IHV12 0 (|L| - i - 1) ? ?) -IHV12 // -HKL /2 width=6/ + lapply (plus_minus_m_m_comm (|L|) d ?) /2/ | normalize /2/ | /2/ ] @@ -90,20 +84,19 @@ lemma tps_weak_all: ∀L,T1,T2,d,e. #L #T1 #T #d #e #HT12 lapply (tps_weak … HT12 0 (d + e) ? ?) -HT12 // #HT12 lapply (tps_weak_top … HT12) // -qed. +qed. (* Basic inversion lemmas ***************************************************) lemma tps_inv_lref1_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → ∀i. T1 = #i → T2 = #i ∨ - ∃∃K,V1,V2,i. d ≤ i & i < d + e & - ↓[O, i] L ≡ K. 𝕓{Abbr} V1 & - K ⊢ V1 [O, d + e - i - 1] ≫ V2 & - ↑[O, i + 1] V2 ≡ T2. + ∃∃K,V,i. d ≤ i & i < d + e & + ↓[O, i] L ≡ K. 𝕓{Abbr} V & + ↑[O, i + 1] V ≡ T2. #L #T1 #T2 #d #e * -L T1 T2 d e [ #L #k #d #e #i #H destruct | /2/ -| #L #K #V1 #V2 #T2 #i #d #e #Hdi #Hide #HLK #HV12 #HVT2 #j #H destruct -i /3 width=9/ +| #L #K #V #T2 #i #d #e #Hdi #Hide #HLK #HVT2 #j #H destruct -i /3 width=7/ | #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct | #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct ] @@ -111,10 +104,9 @@ qed. lemma tps_inv_lref1: ∀L,T2,i,d,e. L ⊢ #i [d, e] ≫ T2 → T2 = #i ∨ - ∃∃K,V1,V2,i. d ≤ i & i < d + e & - ↓[O, i] L ≡ K. 𝕓{Abbr} V1 & - K ⊢ V1 [O, d + e - i - 1] ≫ V2 & - ↑[O, i + 1] V2 ≡ T2. + ∃∃K,V,i. d ≤ i & i < d + e & + ↓[O, i] L ≡ K. 𝕓{Abbr} V & + ↑[O, i + 1] V ≡ T2. /2/ qed. lemma tps_inv_bind1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ≫ U2 → @@ -125,7 +117,7 @@ lemma tps_inv_bind1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ≫ U2 → #d #e #L #U1 #U2 * -d e L U1 U2 [ #L #k #d #e #I #V1 #T1 #H destruct | #L #i #d #e #I #V1 #T1 #H destruct -| #L #K #V #U1 #U2 #i #d #e #_ #_ #_ #_ #_ #I #V1 #T1 #H destruct +| #L #K #V #W #i #d #e #_ #_ #_ #_ #I #V1 #T1 #H destruct | #L #J #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #I #V #T #H destruct /2 width=5/ | #L #J #V1 #V2 #T1 #T2 #d #e #_ #_ #I #V #T #H destruct ] @@ -144,7 +136,7 @@ lemma tps_inv_flat1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ≫ U2 → #d #e #L #U1 #U2 * -d e L U1 U2 [ #L #k #d #e #I #V1 #T1 #H destruct | #L #i #d #e #I #V1 #T1 #H destruct -| #L #K #V #U1 #U2 #i #d #e #_ #_ #_ #_ #_ #I #V1 #T1 #H destruct +| #L #K #V #W #i #d #e #_ #_ #_ #_ #I #V1 #T1 #H destruct | #L #J #V1 #V2 #T1 #T2 #d #e #_ #_ #I #V #T #H destruct | #L #J #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #I #V #T #H destruct /2 width=5/ ] 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 98c73149d..e5ad25ff1 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 @@ -26,16 +26,16 @@ lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → L ⊢ U1 [dt, et] ≫ U2. #K #T1 #T2 #dt #et #H elim H -H K T1 T2 dt et [ #K #k #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ - lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 // + >(lift_mono … H1 … H2) -H1 H2 // | #K #i #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ - lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 // -| #K #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HKV #_ #HV12 #IHV12 #L #U1 #U2 #d #e #HLK #H #HVU2 #Hdetd - lapply (lt_to_le_to_lt … Hidet … Hdetd) #Hid + >(lift_mono … H1 … H2) -H1 H2 // +| #K #KV #V #W #i #dt #et #Hdti #Hidet #HKV #HVW #L #U1 #U2 #d #e #HLK #H #HVU2 #Hdetd + lapply (lt_to_le_to_lt … Hidet … Hdetd) -Hdetd #Hid lapply (lift_inv_lref1_lt … H … Hid) -H #H destruct -U1; - elim (lift_trans_ge … HV12 … HVU2 ?) -HV12 HVU2 V2 // (lift_mono … HVY … HVW) -HVY HVW Y #H destruct -X /2/ | #K #I #V1 #V2 #T1 #T2 #dt #et #_ #_ #IHV12 #IHT12 #L #U1 #U2 #d #e #HLK #H1 #H2 #Hdetd elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct -U1 U2; @@ -54,16 +54,14 @@ lemma tps_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 → L ⊢ U1 [dt + e, et] ≫ U2. #K #T1 #T2 #dt #et #H elim H -H K T1 T2 dt et [ #K #k #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ - lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 // + >(lift_mono … H1 … H2) -H1 H2 // | #K #i #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_ - lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 // -| #K #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HKV #HV1 #HV12 #_ #L #U1 #U2 #d #e #HLK #H #HVU2 #Hddt - <(arith_c1x ? ? ? e) in HV1 #HV1 (**) (* explicit athmetical rewrite and ?'s *) + >(lift_mono … H1 … H2) -H1 H2 // +| #K #KV #V #W #i #dt #et #Hdti #Hidet #HKV #HVW #L #U1 #U2 #d #e #HLK #H #HWU2 #Hddt lapply (transitive_le … Hddt … Hdti) -Hddt #Hid lapply (lift_inv_lref1_ge … H … Hid) -H #H destruct -U1; - lapply (lift_trans_be … HV12 … HVU2 ? ?) -HV12 HVU2 V2 /2/ >plus_plus_comm_23 #HV1U2 - lapply (drop_trans_ge_comm … HLK … HKV ?) -HLK HKV K // -Hid #HLKV - @tps_subst [4,5: /2/ |6,7,8: // |1,2,3: skip ] (**) (* /3 width=8/ is too slow *) + lapply (lift_trans_be … HVW … HWU2 ? ?) -HVW HWU2 W // [ /2/ ] >plus_plus_comm_23 #HVU2 + lapply (drop_trans_ge_comm … HLK … HKV ?) -HLK HKV K // -Hid /3/ | #K #I #V1 #V2 #T1 #T2 #dt #et #_ #_ #IHV12 #IHT12 #L #U1 #U2 #d #e #HLK #H1 #H2 #Hddt elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct -U1 U2; @@ -84,12 +82,11 @@ lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → lapply (lift_inv_sort2 … H) -H #H destruct -T1 /2/ | #L #i #dt #et #K #d #e #_ #T1 #H #_ elim (lift_inv_lref2 … H) -H * #Hid #H destruct -T1 /3/ -| #L #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HLKV #_ #HV12 #IHV12 #K #d #e #HLK #T1 #H #Hdetd - lapply (lt_to_le_to_lt … Hidet … Hdetd) #Hid +| #L #KV #V #W #i #dt #et #Hdti #Hidet #HLKV #HVW #K #d #e #HLK #T1 #H #Hdetd + lapply (lt_to_le_to_lt … Hidet … Hdetd) -Hdetd #Hid lapply (lift_inv_lref2_lt … H … Hid) -H #H destruct -T1; - elim (drop_conf_lt … HLK … HLKV ?) -HLK HLKV L // #L #W #HKL #HKVL #HWV - elim (IHV12 … HKVL … HWV ?) -HKVL HWV /2/ -Hdetd #W1 #HW1 #HWV1 - elim (lift_trans_le … HWV1 … HV12 ?) -HWV1 HV12 V1 // >arith_a2 /3 width=6/ + elim (drop_conf_lt … HLK … HLKV ?) -HLK HLKV L // #L #U #HKL #_ #HUV + elim (lift_trans_le … HUV … HVW ?) -HUV HVW V // >arith_a2 // -Hid /3/ | #L #I #V1 #V2 #U1 #U2 #dt #et #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H #Hdetd elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct -X; elim (IHV12 … HLK … HWV1 ?) -IHV12 // @@ -110,16 +107,15 @@ lemma tps_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 → lapply (lift_inv_sort2 … H) -H #H destruct -T1 /2/ | #L #i #dt #et #K #d #e #_ #T1 #H #_ elim (lift_inv_lref2 … H) -H * #Hid #H destruct -T1 /3/ -| #L #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HLKV #HV1 #HV12 #_ #K #d #e #HLK #T1 #H #Hdedt +| #L #KV #V #W #i #dt #et #Hdti #Hidet #HLKV #HVW #K #d #e #HLK #T1 #H #Hdedt lapply (transitive_le … Hdedt … Hdti) #Hdei lapply (plus_le_weak … Hdedt) -Hdedt #Hedt - lapply (plus_le_weak … Hdei) #Hei - <(arith_h1 ? ? ? e ? ?) in HV1 // #HV1 + lapply (plus_le_weak … Hdei) #Hei lapply (lift_inv_lref2_ge … H … Hdei) -H #H destruct -T1; lapply (drop_conf_ge … HLK … HLKV ?) -HLK HLKV L // #HKV - elim (lift_split … HV12 d (i - e + 1) ? ? ?) -HV12; [2,3,4: normalize /2/ ] -Hdei >arith_e2 // #V0 #HV10 #HV02 + elim (lift_split … HVW d (i - e + 1) ? ? ?) -HVW; [2,3,4: normalize /2/ ] -Hdei >arith_e2 // #V0 #HV10 #HV02 @ex2_1_intro - [2: @tps_subst [4: /2/ |6,7,8: // |1,2,3: skip |5: @arith5 // ] + [2: @tps_subst [3: /2/ |5,6: // |1,2: skip |4: @arith5 // ] |1: skip | // ] (**) (* explicitc constructors *) @@ -141,7 +137,7 @@ lemma tps_inv_lift1_eq: ∀L,U1,U2,d,e. #L #U1 #U2 #d #e #H elim H -H L U1 U2 d e [ // | // -| #L #K #V #V1 #V2 #i #d #e #Hdi #Hide #_ #_ #_ #_ #T1 #H +| #L #K #V #W #i #d #e #Hdi #Hide #_ #_ #T1 #H elim (lift_inv_lref2 … H) -H * #H [ lapply (le_to_lt_to_lt … Hdi … H) -Hdi H #H elim (lt_refl_false … H) diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_split.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_split.ma index 041bb0c98..6bb476fcd 100644 --- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_split.ma +++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_split.ma @@ -23,19 +23,13 @@ lemma tps_split_up: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → ∀i. d ≤ i → #L #T1 #T2 #d #e #H elim H -L T1 T2 d e [ /2/ | /2/ -| #L #K #V #V1 #V2 #i #d #e #Hdi #Hide #HLK #HV1 #HV12 #IHV12 #j #Hdj #Hjde - elim (lt_or_ge i j) #Hij - [ -HV1 Hide; - lapply (drop_fwd_drop2 … HLK) #HLK' - elim (IHV12 (j - i - 1) ? ?) -IHV12; normalize /2/ -Hjde arith_b2 // #W1 #HVW1 #HWV1 - generalize in match HVW1 generalize in match Hij -HVW1 (**) (* rewriting in the premises, rewrites in the goal too *) - >(plus_minus_m_m_comm … Hdj) in ⊢ (% → % → ?) -Hdj #Hij' #HVW1 - elim (lift_total W1 0 (i + 1)) #W2 #HW12 - lapply (tps_lift_ge … HWV1 … HLK' HW12 HV12 ?) -HWV1 HLK' HV12 // >arith_a2 /3 width=6/ - | -IHV12 Hdi Hdj; - generalize in match HV1 generalize in match Hide -HV1 Hide (**) (* rewriting in the premises, rewrites in the goal too *) - >(plus_minus_m_m_comm … Hjde) in ⊢ (% → % → ?) -Hjde #Hide #HV1 - @ex2_1_intro [2: @tps_lref |1: skip | /2 width=6/ ] (**) (* /3 width=6 is too slow *) +| #L #K #V #W #i #d #e #Hdi #Hide #HLK #HVW #j #Hdj #Hjde + elim (lt_or_ge i j) + [ -Hide Hjde; + >(plus_minus_m_m_comm j d) in ⊢ (% → ?) // -Hdj /3/ + | -Hdi Hdj; #Hid + generalize in match Hide -Hide (**) (* rewriting in the premises, rewrites in the goal too *) + >(plus_minus_m_m_comm … Hjde) in ⊢ (% → ?) -Hjde /4/ ] | #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #i #Hdi #Hide elim (IHV12 i ? ?) -IHV12 // #V #HV1 #HV2 diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma index 857bc7ebe..1e3c3629a 100644 --- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma +++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma @@ -36,14 +36,13 @@ theorem tps_trans: ∀L,T1,T,d,e. L ⊢ T1 [d, e] ≫ T → ∀T2. L ⊢ T [d, e qed. *) -axiom tps_conf_subst_subst_lt: ∀L,K1,V1,W1,T1,i1,d,e,T2,K2,V2,W2,i2. +axiom tps_conf_subst_subst_lt: ∀L,K1,V1,T1,i1,d,e,T2,K2,V2,i2. ↓[O, i1] L ≡ K1. 𝕓{Abbr} V1 → ↓[O, i2] L≡ K2. 𝕓{Abbr} V2 → - K1 ⊢ V1 [O, d + e - i1 - 1] ≫ W1 → K2 ⊢ V2 [O, d + e - i2 - 1] ≫ W2 → - ↑[O, i1 + 1] W1 ≡ T1 → ↑[O, i2 + 1] W2 ≡ T2 → + ↑[O, i1 + 1] V1 ≡ T1 → ↑[O, i2 + 1] V2 ≡ T2 → d ≤ i1 → i1 < d + e → d ≤ i2 → i2 < d + e → i1 < i2 → ∃∃T. L ⊢ T1 [d, e] ≫ T & L ⊢ T2 [d, e] ≫ T. (* -#L #K1 #V1 #W1 #T1 #i1 #d #e #T2 #K2 #V2 #W2 #i2 +#L #K1 #V1 #T1 #i1 #d #e #T2 #K2 #V2 #i2 #HLK1 #HLK2 #HVW1 #HVW2 #HWT1 #HWT2 #Hdi1 #Hi1de #Hdi2 #Hi2de #Hi12 *) @@ -52,25 +51,16 @@ theorem tps_conf: ∀L,T0,T1,d,e. L ⊢ T0 [d, e] ≫ T1 → ∀T2. L ⊢ T0 [d, #L #T0 #T1 #d #e #H elim H -H L T0 T1 d e [ /2/ | /2/ -| #L #K1 #V1 #W1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVW1 #HWT1 #IHVW1 #T2 #H +| #L #K1 #V1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVT1 #T2 #H elim (tps_inv_lref1 … H) -H - [ -IHVW1 #HX destruct -T2 - @ex2_1_intro [2: // | skip ] /2 width=6/ (**) (* /3 width=9/ is slow *) - | * #K2 #V2 #W2 #i2 #Hdi2 #Hi2de #HLK2 #HVW2 #HWT2 + [ #HX destruct -T2 /4/ + | * #K2 #V2 #i2 #Hdi2 #Hi2de #HLK2 #HVT2 elim (lt_or_eq_or_gt i1 i2) #Hi12 - [ @tps_conf_subst_subst_lt /width=19/ - | -HVW1; destruct -i2; - lapply (transitive_le ? ? (i1 + 1) Hdi2 ?) -Hdi2 // #Hdi2 - lapply (drop_mono … HLK1 … HLK2) -HLK1 Hdi1 Hi1de #H destruct -V1 K1; - elim (IHVW1 … HVW2) -IHVW1 HVW2 #W #HW1 #HW2 - lapply (drop_fwd_drop2 … HLK2) -HLK2 #HLK2 - elim (lift_total W 0 (i1 + 1)) #T #HWT - lapply (tps_lift_ge … HW1 … HLK2 HWT1 HWT ?) -HW1 HWT1 // - lapply (tps_lift_ge … HW2 … HLK2 HWT2 HWT ?) -HW2 HWT2 HLK2 HWT // normalize #HT2 #HT1 - lapply (tps_weak … HT1 d e ? ?) -HT1 [ >arith_i2 // | // ] - lapply (tps_weak … HT2 d e ? ?) -HT2 [ >arith_i2 // | // ] - /2/ - | @ex2_1_comm @tps_conf_subst_subst_lt /width=19/ + [ @tps_conf_subst_subst_lt /width=15/ + | -Hdi2 Hi2de; destruct -i2; + lapply (drop_mono … HLK1 … HLK2) -HLK1 #H destruct -V1 K1 + >(lift_mono … HVT1 … HVT2) -HVT1 /2/ + | @ex2_1_comm @tps_conf_subst_subst_lt /width=15/ ] ] | #L #I #V0 #V1 #T0 #T1 #d #e #_ #_ #IHV01 #IHT01 #X #HX -- 2.39.2