X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fcnv_preserve_sub.ma;h=6239b4798b1c44abb73d3afbb9d0c4c0e7b38e0b;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=c99d6a5c08a7387f6416eee775775f3b520f73fd;hpb=b98ec1a1a37602eca524dc5487c357a200bbb5b6;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma index c99d6a5c0..6239b4798 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma @@ -19,53 +19,53 @@ include "basic_2/dynamic/cnv.ma". (* Inductive premises for the preservation results **************************) -definition IH_cnv_cpm_trans_lpr (a) (h): relation3 genv lenv term ≝ - λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] → - ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡[n,h] T2 → - ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h]. +definition IH_cnv_cpm_trans_lpr (h) (a): relation3 genv lenv term ≝ + λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] → + ∀n,T2. ❪G,L1❫ ⊢ T1 ➡[h,n] T2 → + ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a]. -definition IH_cnv_cpms_trans_lpr (a) (h): relation3 genv lenv term ≝ - λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] → - ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 → - ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h]. +definition IH_cnv_cpms_trans_lpr (h) (a): relation3 genv lenv term ≝ + λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] → + ∀n,T2. ❪G,L1❫ ⊢ T1 ➡*[h,n] T2 → + ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a]. -definition IH_cnv_cpm_conf_lpr (a) (h): relation3 genv lenv term ≝ - λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] → - ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 → - ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 → - ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T. +definition IH_cnv_cpm_conf_lpr (h) (a): relation3 genv lenv term ≝ + λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] → + ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 → + ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 → + ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T. -definition IH_cnv_cpms_strip_lpr (a) (h): relation3 genv lenv term ≝ - λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] → - ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 → - ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 → - ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T. +definition IH_cnv_cpms_strip_lpr (h) (a): relation3 genv lenv term ≝ + λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] → + ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 → + ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 → + ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T. -definition IH_cnv_cpms_conf_lpr (a) (h): relation3 genv lenv term ≝ - λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] → - ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h] T2 → - ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 → - ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T. +definition IH_cnv_cpms_conf_lpr (h) (a): relation3 genv lenv term ≝ + λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] → + ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡*[h,n2] T2 → + ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 → + ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T. (* Auxiliary properties for preservation ************************************) -fact cnv_cpms_trans_lpr_sub (a) (h) (o): - ∀G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) → - ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_trans_lpr a h G1 L1 T1. -#a #h #o #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H +fact cnv_cpms_trans_lpr_sub (h) (a): + ∀G0,L0,T0. + (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) → + ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_trans_lpr h a G1 L1 T1. +#h #a #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H @(cpms_ind_dx … H) -n -T2 /3 width=7 by fpbg_cpms_trans/ qed-. -fact cnv_cpm_conf_lpr_sub (a) (h) (o): - ∀G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) → - ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_conf_lpr a h G1 L1 T1. +fact cnv_cpm_conf_lpr_sub (h) (a): + ∀G0,L0,T0. + (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) → + ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_conf_lpr h a G1 L1 T1. /3 width=8 by cpm_cpms/ qed-. -fact cnv_cpms_strip_lpr_sub (a) (h) (o): - ∀G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) → - ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1. +fact cnv_cpms_strip_lpr_sub (h) (a): + ∀G0,L0,T0. + (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) → + ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_strip_lpr h a G1 L1 T1. /3 width=8 by cpm_cpms/ qed-.