X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Ftps.ma;h=11edc90b10b800e78d8c672e3af12d73c5781bb6;hb=ef3bdc4be26f6518a82a79c64e986253f7aeaa3c;hp=8a5dc13d083afa67e25924771bdb769e7b881d04;hpb=39e80f80b26e18cf78f805e814ba2f2e8400c1f1;p=helm.git 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 8a5dc13d0..11edc90b1 100644 --- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps.ma +++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps.ma @@ -18,15 +18,15 @@ include "Basic_2/substitution/ldrop.ma". (* PARALLEL SUBSTITUTION ON TERMS *******************************************) inductive tps: nat → nat → lenv → relation term ≝ -| tps_atom : ∀L,I,d,e. tps d e L (𝕒{I}) (𝕒{I}) +| tps_atom : ∀L,I,d,e. tps d e L (⓪{I}) (⓪{I}) | 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 d e L (#i) W + ⇩[0, i] L ≡ K. ⓓV → ⇧[0, i + 1] V ≡ W → tps d e L (#i) W | tps_bind : ∀L,I,V1,V2,T1,T2,d,e. - tps d e L V1 V2 → tps (d + 1) e (L. 𝕓{I} V2) T1 T2 → - tps d e L (𝕓{I} V1. T1) (𝕓{I} V2. T2) + tps d e L V1 V2 → tps (d + 1) e (L. ⓑ{I} V2) T1 T2 → + tps d e L (ⓑ{I} V1. T1) (ⓑ{I} V2. T2) | tps_flat : ∀L,I,V1,V2,T1,T2,d,e. tps d e L V1 V2 → tps d e L T1 T2 → - tps d e L (𝕗{I} V1. T1) (𝕗{I} V2. T2) + tps d e L (ⓕ{I} V1. T1) (ⓕ{I} V2. T2) . interpretation "parallel substritution (term)" @@ -51,7 +51,7 @@ lemma tps_refl: ∀T,L,d,e. L ⊢ T [d, e] ▶ T. qed. (* Basic_1: was: subst1_ex *) -lemma tps_full: ∀K,V,T1,L,d. ⇩[0, d] L ≡ (K. 𝕓{Abbr} V) → +lemma tps_full: ∀K,V,T1,L,d. ⇩[0, d] L ≡ (K. ⓓV) → ∃∃T2,T. L ⊢ T1 [d, 1] ▶ T2 & ⇧[d, 1] T ≡ T2. #K #V #T1 elim T1 -T1 [ * #i #L #d #HLK /2 width=4/ @@ -61,7 +61,7 @@ lemma tps_full: ∀K,V,T1,L,d. ⇩[0, d] L ≡ (K. 𝕓{Abbr} V) → elim (lift_split … HVW i i ? ? ?) // /3 width=4/ | * #I #W1 #U1 #IHW1 #IHU1 #L #d #HLK elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2 - [ elim (IHU1 (L. 𝕓{I} W2) (d+1) ?) -IHU1 /2 width=1/ -HLK /3 width=8/ + [ elim (IHU1 (L. ⓑ{I} W2) (d+1) ?) -IHU1 /2 width=1/ -HLK /3 width=8/ | elim (IHU1 … HLK) -IHU1 -HLK /3 width=8/ ] ] @@ -115,7 +115,7 @@ lemma tps_split_up: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶ T2 → ∀i. d ≤ i → elim (IHV12 i ? ?) -IHV12 // #V #HV1 #HV2 elim (IHT12 (i + 1) ? ?) -IHT12 /2 width=1/ -Hdi -Hide >arith_c1x #T #HT1 #HT2 - lapply (tps_lsubs_conf … HT1 (L. 𝕓{I} V) ?) -HT1 /3 width=5/ + lapply (tps_lsubs_conf … HT1 (L. ⓑ{I} V) ?) -HT1 /3 width=5/ | #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #i #Hdi #Hide elim (IHV12 i ? ?) -IHV12 // elim (IHT12 i ? ?) -IHT12 // -Hdi -Hide /3 width=5/ @@ -124,10 +124,10 @@ qed. (* Basic inversion lemmas ***************************************************) -fact tps_inv_atom1_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶ T2 → ∀I. T1 = 𝕒{I} → - T2 = 𝕒{I} ∨ +fact tps_inv_atom1_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶ T2 → ∀I. T1 = ⓪{I} → + T2 = ⓪{I} ∨ ∃∃K,V,i. d ≤ i & i < d + e & - ⇩[O, i] L ≡ K. 𝕓{Abbr} V & + ⇩[O, i] L ≡ K. ⓓV & ⇧[O, i + 1] V ≡ T2 & I = LRef i. #L #T1 #T2 #d #e * -L -T1 -T2 -d -e @@ -138,10 +138,10 @@ fact tps_inv_atom1_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶ T2 → ∀I. T1 = ] qed. -lemma tps_inv_atom1: ∀L,T2,I,d,e. L ⊢ 𝕒{I} [d, e] ▶ T2 → - T2 = 𝕒{I} ∨ +lemma tps_inv_atom1: ∀L,T2,I,d,e. L ⊢ ⓪{I} [d, e] ▶ T2 → + T2 = ⓪{I} ∨ ∃∃K,V,i. d ≤ i & i < d + e & - ⇩[O, i] L ≡ K. 𝕓{Abbr} V & + ⇩[O, i] L ≡ K. ⓓV & ⇧[O, i + 1] V ≡ T2 & I = LRef i. /2 width=3/ qed-. @@ -158,7 +158,7 @@ qed-. lemma tps_inv_lref1: ∀L,T2,i,d,e. L ⊢ #i [d, e] ▶ T2 → T2 = #i ∨ ∃∃K,V. d ≤ i & i < d + e & - ⇩[O, i] L ≡ K. 𝕓{Abbr} V & + ⇩[O, i] L ≡ K. ⓓV & ⇧[O, i + 1] V ≡ T2. #L #T2 #i #d #e #H elim (tps_inv_atom1 … H) -H /2 width=1/ @@ -172,10 +172,10 @@ elim (tps_inv_atom1 … H) -H // qed-. fact tps_inv_bind1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ▶ U2 → - ∀I,V1,T1. U1 = 𝕓{I} V1. T1 → + ∀I,V1,T1. U1 = ⓑ{I} V1. T1 → ∃∃V2,T2. L ⊢ V1 [d, e] ▶ V2 & - L. 𝕓{I} V2 ⊢ T1 [d + 1, e] ▶ T2 & - U2 = 𝕓{I} V2. T2. + L. ⓑ{I} V2 ⊢ T1 [d + 1, e] ▶ T2 & + U2 = ⓑ{I} V2. T2. #d #e #L #U1 #U2 * -d -e -L -U1 -U2 [ #L #k #d #e #I #V1 #T1 #H destruct | #L #K #V #W #i #d #e #_ #_ #_ #_ #I #V1 #T1 #H destruct @@ -184,16 +184,16 @@ fact tps_inv_bind1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ▶ U2 → ] qed. -lemma tps_inv_bind1: ∀d,e,L,I,V1,T1,U2. L ⊢ 𝕓{I} V1. T1 [d, e] ▶ U2 → +lemma tps_inv_bind1: ∀d,e,L,I,V1,T1,U2. L ⊢ ⓑ{I} V1. T1 [d, e] ▶ U2 → ∃∃V2,T2. L ⊢ V1 [d, e] ▶ V2 & - L. 𝕓{I} V2 ⊢ T1 [d + 1, e] ▶ T2 & - U2 = 𝕓{I} V2. T2. + L. ⓑ{I} V2 ⊢ T1 [d + 1, e] ▶ T2 & + U2 = ⓑ{I} V2. T2. /2 width=3/ qed-. fact tps_inv_flat1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ▶ U2 → - ∀I,V1,T1. U1 = 𝕗{I} V1. T1 → + ∀I,V1,T1. U1 = ⓕ{I} V1. T1 → ∃∃V2,T2. L ⊢ V1 [d, e] ▶ V2 & L ⊢ T1 [d, e] ▶ T2 & - U2 = 𝕗{I} V2. T2. + U2 = ⓕ{I} V2. T2. #d #e #L #U1 #U2 * -d -e -L -U1 -U2 [ #L #k #d #e #I #V1 #T1 #H destruct | #L #K #V #W #i #d #e #_ #_ #_ #_ #I #V1 #T1 #H destruct @@ -202,9 +202,9 @@ fact tps_inv_flat1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ▶ U2 → ] qed. -lemma tps_inv_flat1: ∀d,e,L,I,V1,T1,U2. L ⊢ 𝕗{I} V1. T1 [d, e] ▶ U2 → +lemma tps_inv_flat1: ∀d,e,L,I,V1,T1,U2. L ⊢ ⓕ{I} V1. T1 [d, e] ▶ U2 → ∃∃V2,T2. L ⊢ V1 [d, e] ▶ V2 & L ⊢ T1 [d, e] ▶ T2 & - U2 = 𝕗{I} V2. T2. + U2 = ⓕ{I} V2. T2. /2 width=3/ qed-. fact tps_inv_refl_O2_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶ T2 → e = 0 → T1 = T2.