X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpr.ma;h=b99663e05ee843c231c29a44359e3be07a8e61b6;hp=2d0608f9237369077ceb79b172fed79fbbc71e0c;hb=ca7327c20c6031829fade8bb84a3a1bb66113f54;hpb=25c634037771dff0138e5e8e3d4378183ff49b86 diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma index 2d0608f92..b99663e05 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma @@ -25,24 +25,24 @@ include "basic_2/rt_transition/cpm.ma". (* Note: cpr_flat: does not hold in basic_1 *) (* Basic_1: includes: pr2_thin_dx *) lemma cpr_flat: ∀h,I,G,L,V1,V2,T1,T2. - ❪G,L❫ ⊢ V1 ➡[h] V2 → ❪G,L❫ ⊢ T1 ➡[h] T2 → - ❪G,L❫ ⊢ ⓕ[I]V1.T1 ➡[h] ⓕ[I]V2.T2. + ❪G,L❫ ⊢ V1 ➡[h,0] V2 → ❪G,L❫ ⊢ T1 ➡[h,0] T2 → + ❪G,L❫ ⊢ ⓕ[I]V1.T1 ➡[h,0] ⓕ[I]V2.T2. #h * /2 width=1 by cpm_cast, cpm_appl/ qed. (* Basic_1: was: pr2_head_1 *) -lemma cpr_pair_sn: ∀h,I,G,L,V1,V2. ❪G,L❫ ⊢ V1 ➡[h] V2 → - ∀T. ❪G,L❫ ⊢ ②[I]V1.T ➡[h] ②[I]V2.T. +lemma cpr_pair_sn: ∀h,I,G,L,V1,V2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 → + ∀T. ❪G,L❫ ⊢ ②[I]V1.T ➡[h,0] ②[I]V2.T. #h * /2 width=1 by cpm_bind, cpr_flat/ qed. (* Basic inversion properties ***********************************************) -lemma cpr_inv_atom1: ∀h,J,G,L,T2. ❪G,L❫ ⊢ ⓪[J] ➡[h] T2 → +lemma cpr_inv_atom1: ∀h,J,G,L,T2. ❪G,L❫ ⊢ ⓪[J] ➡[h,0] T2 → ∨∨ T2 = ⓪[J] - | ∃∃K,V1,V2. ❪G,K❫ ⊢ V1 ➡[h] V2 & ⇧[1] V2 ≘ T2 & + | ∃∃K,V1,V2. ❪G,K❫ ⊢ V1 ➡[h,0] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓓV1 & J = LRef 0 - | ∃∃I,K,T,i. ❪G,K❫ ⊢ #i ➡[h] T & ⇧[1] T ≘ T2 & + | ∃∃I,K,T,i. ❪G,K❫ ⊢ #i ➡[h,0] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I] & J = LRef (↑i). #h #J #G #L #T2 #H elim (cpm_inv_atom1 … H) -H * [2,4:|*: /3 width=8 by or3_intro0, or3_intro1, or3_intro2, ex4_4_intro, ex4_3_intro/ ] @@ -52,48 +52,48 @@ lemma cpr_inv_atom1: ∀h,J,G,L,T2. ❪G,L❫ ⊢ ⓪[J] ➡[h] T2 → qed-. (* Basic_1: includes: pr0_gen_sort pr2_gen_sort *) -lemma cpr_inv_sort1: ∀h,G,L,T2,s. ❪G,L❫ ⊢ ⋆s ➡[h] T2 → T2 = ⋆s. +lemma cpr_inv_sort1: ∀h,G,L,T2,s. ❪G,L❫ ⊢ ⋆s ➡[h,0] T2 → T2 = ⋆s. #h #G #L #T2 #s #H elim (cpm_inv_sort1 … H) -H // qed-. -lemma cpr_inv_zero1: ∀h,G,L,T2. ❪G,L❫ ⊢ #0 ➡[h] T2 → +lemma cpr_inv_zero1: ∀h,G,L,T2. ❪G,L❫ ⊢ #0 ➡[h,0] T2 → ∨∨ T2 = #0 - | ∃∃K,V1,V2. ❪G,K❫ ⊢ V1 ➡[h] V2 & ⇧[1] V2 ≘ T2 & + | ∃∃K,V1,V2. ❪G,K❫ ⊢ V1 ➡[h,0] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓓV1. #h #G #L #T2 #H elim (cpm_inv_zero1 … H) -H * /3 width=6 by ex3_3_intro, or_introl, or_intror/ #n #K #V1 #V2 #_ #_ #_ #H destruct qed-. -lemma cpr_inv_lref1: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #↑i ➡[h] T2 → +lemma cpr_inv_lref1: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #↑i ➡[h,0] T2 → ∨∨ T2 = #(↑i) - | ∃∃I,K,T. ❪G,K❫ ⊢ #i ➡[h] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I]. + | ∃∃I,K,T. ❪G,K❫ ⊢ #i ➡[h,0] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I]. #h #G #L #T2 #i #H elim (cpm_inv_lref1 … H) -H * /3 width=6 by ex3_3_intro, or_introl, or_intror/ qed-. -lemma cpr_inv_gref1: ∀h,G,L,T2,l. ❪G,L❫ ⊢ §l ➡[h] T2 → T2 = §l. +lemma cpr_inv_gref1: ∀h,G,L,T2,l. ❪G,L❫ ⊢ §l ➡[h,0] T2 → T2 = §l. #h #G #L #T2 #l #H elim (cpm_inv_gref1 … H) -H // qed-. (* Basic_1: includes: pr0_gen_cast pr2_gen_cast *) -lemma cpr_inv_cast1: ∀h,G,L,V1,U1,U2. ❪G,L❫ ⊢ ⓝ V1.U1 ➡[h] U2 → - ∨∨ ∃∃V2,T2. ❪G,L❫ ⊢ V1 ➡[h] V2 & ❪G,L❫ ⊢ U1 ➡[h] T2 & +lemma cpr_inv_cast1: ∀h,G,L,V1,U1,U2. ❪G,L❫ ⊢ ⓝ V1.U1 ➡[h,0] U2 → + ∨∨ ∃∃V2,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 & ❪G,L❫ ⊢ U1 ➡[h,0] T2 & U2 = ⓝV2.T2 - | ❪G,L❫ ⊢ U1 ➡[h] U2. + | ❪G,L❫ ⊢ U1 ➡[h,0] U2. #h #G #L #V1 #U1 #U2 #H elim (cpm_inv_cast1 … H) -H /2 width=1 by or_introl, or_intror/ * #n #_ #H destruct qed-. -lemma cpr_inv_flat1: ∀h,I,G,L,V1,U1,U2. ❪G,L❫ ⊢ ⓕ[I]V1.U1 ➡[h] U2 → - ∨∨ ∃∃V2,T2. ❪G,L❫ ⊢ V1 ➡[h] V2 & ❪G,L❫ ⊢ U1 ➡[h] T2 & +lemma cpr_inv_flat1: ∀h,I,G,L,V1,U1,U2. ❪G,L❫ ⊢ ⓕ[I]V1.U1 ➡[h,0] U2 → + ∨∨ ∃∃V2,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 & ❪G,L❫ ⊢ U1 ➡[h,0] T2 & U2 = ⓕ[I]V2.T2 - | (❪G,L❫ ⊢ U1 ➡[h] U2 ∧ I = Cast) - | ∃∃p,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h] V2 & ❪G,L❫ ⊢ W1 ➡[h] W2 & - ❪G,L.ⓛW1❫ ⊢ T1 ➡[h] T2 & U1 = ⓛ[p]W1.T1 & + | (❪G,L❫ ⊢ U1 ➡[h,0] U2 ∧ I = Cast) + | ∃∃p,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 & ❪G,L❫ ⊢ W1 ➡[h,0] W2 & + ❪G,L.ⓛW1❫ ⊢ T1 ➡[h,0] T2 & U1 = ⓛ[p]W1.T1 & U2 = ⓓ[p]ⓝW2.V2.T2 & I = Appl - | ∃∃p,V,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h] V & ⇧[1] V ≘ V2 & - ❪G,L❫ ⊢ W1 ➡[h] W2 & ❪G,L.ⓓW1❫ ⊢ T1 ➡[h] T2 & + | ∃∃p,V,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V & ⇧[1] V ≘ V2 & + ❪G,L❫ ⊢ W1 ➡[h,0] W2 & ❪G,L.ⓓW1❫ ⊢ T1 ➡[h,0] T2 & U1 = ⓓ[p]W1.T1 & U2 = ⓓ[p]W2.ⓐV2.T2 & I = Appl. #h * #G #L #V1 #U1 #U2 #H @@ -108,26 +108,26 @@ qed-. lemma cpr_ind (h): ∀Q:relation4 genv lenv term term. (∀I,G,L. Q G L (⓪[I]) (⓪[I])) → - (∀G,K,V1,V2,W2. ❪G,K❫ ⊢ V1 ➡[h] V2 → Q G K V1 V2 → + (∀G,K,V1,V2,W2. ❪G,K❫ ⊢ V1 ➡[h,0] V2 → Q G K V1 V2 → ⇧[1] V2 ≘ W2 → Q G (K.ⓓV1) (#0) W2 - ) → (∀I,G,K,T,U,i. ❪G,K❫ ⊢ #i ➡[h] T → Q G K (#i) T → + ) → (∀I,G,K,T,U,i. ❪G,K❫ ⊢ #i ➡[h,0] T → Q G K (#i) T → ⇧[1] T ≘ U → Q G (K.ⓘ[I]) (#↑i) (U) - ) → (∀p,I,G,L,V1,V2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h] V2 → ❪G,L.ⓑ[I]V1❫ ⊢ T1 ➡[h] T2 → + ) → (∀p,I,G,L,V1,V2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 → ❪G,L.ⓑ[I]V1❫ ⊢ T1 ➡[h,0] T2 → Q G L V1 V2 → Q G (L.ⓑ[I]V1) T1 T2 → Q G L (ⓑ[p,I]V1.T1) (ⓑ[p,I]V2.T2) - ) → (∀I,G,L,V1,V2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h] V2 → ❪G,L❫ ⊢ T1 ➡[h] T2 → + ) → (∀I,G,L,V1,V2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 → ❪G,L❫ ⊢ T1 ➡[h,0] T2 → Q G L V1 V2 → Q G L T1 T2 → Q G L (ⓕ[I]V1.T1) (ⓕ[I]V2.T2) - ) → (∀G,L,V,T1,T,T2. ⇧[1] T ≘ T1 → ❪G,L❫ ⊢ T ➡[h] T2 → + ) → (∀G,L,V,T1,T,T2. ⇧[1] T ≘ T1 → ❪G,L❫ ⊢ T ➡[h,0] T2 → Q G L T T2 → Q G L (+ⓓV.T1) T2 - ) → (∀G,L,V,T1,T2. ❪G,L❫ ⊢ T1 ➡[h] T2 → Q G L T1 T2 → + ) → (∀G,L,V,T1,T2. ❪G,L❫ ⊢ T1 ➡[h,0] T2 → Q G L T1 T2 → Q G L (ⓝV.T1) T2 - ) → (∀p,G,L,V1,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h] V2 → ❪G,L❫ ⊢ W1 ➡[h] W2 → ❪G,L.ⓛW1❫ ⊢ T1 ➡[h] T2 → + ) → (∀p,G,L,V1,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V2 → ❪G,L❫ ⊢ W1 ➡[h,0] W2 → ❪G,L.ⓛW1❫ ⊢ T1 ➡[h,0] T2 → Q G L V1 V2 → Q G L W1 W2 → Q G (L.ⓛW1) T1 T2 → Q G L (ⓐV1.ⓛ[p]W1.T1) (ⓓ[p]ⓝW2.V2.T2) - ) → (∀p,G,L,V1,V,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h] V → ❪G,L❫ ⊢ W1 ➡[h] W2 → ❪G,L.ⓓW1❫ ⊢ T1 ➡[h] T2 → + ) → (∀p,G,L,V1,V,V2,W1,W2,T1,T2. ❪G,L❫ ⊢ V1 ➡[h,0] V → ❪G,L❫ ⊢ W1 ➡[h,0] W2 → ❪G,L.ⓓW1❫ ⊢ T1 ➡[h,0] T2 → Q G L V1 V → Q G L W1 W2 → Q G (L.ⓓW1) T1 T2 → ⇧[1] V ≘ V2 → Q G L (ⓐV1.ⓓ[p]W1.T1) (ⓓ[p]W2.ⓐV2.T2) ) → - ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡[h] T2 → Q G L T1 T2. + ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡[h,0] T2 → Q G L T1 T2. #h #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #IH8 #IH9 #G #L #T1 #T2 @(insert_eq_0 … 0) #n #H @(cpm_ind … H) -G -L -T1 -T2 -n [2,4,11:|*: /3 width=4 by/ ]