update in static_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpms_conf.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma
index e6fb158e62cd011ace4c7d5d2ac962a175cd64f7..a86d5c311007be6bf46fe8000dbe4c3705015483 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma
@@ -12,36 +12,51 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predstar_7.ma".
 include "basic_2/dynamic/cnv_cpm_trans.ma".
 include "basic_2/dynamic/cnv_cpm_conf.ma".
+include "basic_2/dynamic/cnv_cpms_tdpos.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
-definition cpsms (n) (h) (o): relation4 genv lenv term term ≝ λG,L,T1,T2.
-                 ∃∃n1,n2,T. T1 ≛[h,o] T → ⊥ & ⦃G, L⦄ ⊢ T1 ➡[n1,h] T & ⦃G, L⦄ ⊢ T ➡*[n2,h] T2 & n1+n2 = n.
-
-interpretation
-   "context-sensitive parallel stratified t-bound  rt-computarion (term)"
-   'PRedStar n h o G L T1 T2 = (cpsms n h o G L T1 T2).
+(* Sub confluence propery with t-bound rt-computation for terms *************)
 
-definition IH_cnv_cpsms_conf_lpr (a) (h) (o): relation3 genv lenv term ≝
-                                 λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
-                                 ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h,o] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h,o] 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.
+fact cnv_cpms_conf_lpr_refl_refl_aux (h) (G0) (L1) (L2) (T0:term):
+     ∃∃T. ⦃G0,L1⦄ ⊢ T0 ➡*[h] T & ⦃G0,L2⦄ ⊢ T0 ➡*[h] T.
+/2 width=3 by ex2_intro/ qed-.
 
-(* Sub confluence propery with t-bound rt-computation for terms *************)
+fact cnv_cpms_conf_lpr_refl_step_aux (a) (h) (o) (G0) (L0) (T0) (m21) (m22):
+     (∀G,L,T. ⦃G0,L0,T0⦄ >[h,o] ⦃G,L,T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
+     (∀G,L,T. ⦃G0,L0,T0⦄ >[h,o] ⦃G,L,T⦄ → IH_cnv_cpms_conf_lpr a h G L T) →
+     ⦃G0,L0⦄ ⊢ T0 ![a,h] →
+     ∀X2. ⦃G0,L0⦄ ⊢ T0 ➡[m21,h] X2 → (T0 ≛[h,o] X2 → ⊥) → ∀T2. ⦃G0,L0⦄ ⊢ X2 ➡*[m22,h] T2 →
+     ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
+     ∃∃T. ⦃G0,L1⦄ ⊢ T0 ➡*[m21+m22,h] T& ⦃G0,L2⦄ ⊢ T2 ➡*[h] T.
+#a #h #o #G0 #L0 #T0 #m21 #m22 #IH2 #IH1 #H0
+#X2 #HX02 #HnX02 #T2 #HXT2
+#L1 #HL01 #L2 #HL02
+lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX02 … L0 ?) // #HX2
+elim (cnv_cpm_conf_lpr_aux … IH2 IH1 … HX02 … 0 T0 … L0 … HL01) //
+<minus_n_O <minus_O_n #Y1 #HXY1 #HTY1
+elim (cnv_cpms_strip_lpr_sub … IH1 … HXT2 0 X2 … HL02 L0) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ]
+<minus_n_O <minus_O_n #Y2 #HTY2 #HXY2 -HXT2
+elim (IH1 … HXY1 … HXY2 … HL01 … HL02) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ]
+-a -o -L0 -X2 <minus_n_O <minus_O_n #Y #HY1 #HY2
+lapply (cpms_trans … HTY1 … HY1) -Y1 #HT0Y
+lapply (cpms_trans … HTY2 … HY2) -Y2 #HT2Y
+/2 width=3 by ex2_intro/
+qed-.
 
-fact cnv_cpsms_conf_lpr_aux (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_conf_lpr a h G1 L1 T1) →
-                            ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpsms_conf_lpr a h o G1 L1 T1.
-#a #h #o #G #L #T #IH2 #IH1 #G0 #L0 #T0 #HG #HL #HT #HT0
-#n1 #T1 * #m11 #m12 #X1 #HnX01 #HX01 #HXT1 #H1
-#n2 #T2 * #m21 #m22 #X2 #HnX02 #HX02 #HXT2 #H2
-#L1 #HL01 #L2 #HL02 destruct
+fact cnv_cpms_conf_lpr_step_step_aux (a) (h) (o) (G0) (L0) (T0) (m11) (m12) (m21) (m22):
+     (∀G,L,T. ⦃G0,L0,T0⦄ >[h,o] ⦃G,L,T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
+     (∀G,L,T. ⦃G0,L0,T0⦄ >[h,o] ⦃G,L,T⦄ → IH_cnv_cpms_conf_lpr a h G L T) →
+     ⦃G0,L0⦄ ⊢ T0 ![a,h] →
+     ∀X1. ⦃G0,L0⦄ ⊢ T0 ➡[m11,h] X1 → (T0 ≛[h,o] X1 → ⊥) → ∀T1. ⦃G0,L0⦄ ⊢ X1 ➡*[m12,h] T1 →
+     ∀X2. ⦃G0,L0⦄ ⊢ T0 ➡[m21,h] X2 → (T0 ≛[h,o] X2 → ⊥) → ∀T2. ⦃G0,L0⦄ ⊢ X2 ➡*[m22,h] T2 →
+     ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
+     ∃∃T. ⦃G0,L1⦄ ⊢ T1 ➡*[m21+m22-(m11+m12),h] T& ⦃G0,L2⦄ ⊢ T2 ➡*[m11+m12-(m21+m22),h] T.
+#a #h #o #G0 #L0 #T0 #m11 #m12 #m21 #m22 #IH2 #IH1 #H0
+#X1 #HX01 #HnX01 #T1 #HXT1 #X2 #HX02 #HnX02 #T2 #HXT2
+#L1 #HL01 #L2 #HL02
 lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX01 … L0 ?) // #HX1
 lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX02 … L0 ?) // #HX2
 elim (cnv_cpm_conf_lpr_aux … IH2 IH1 … HX01 … HX02 … L0 … L0) // #Z0 #HXZ10 #HXZ20
@@ -55,3 +70,27 @@ lapply (cpms_trans … HTZ1 … HZ01) -Z1 <arith_l4 #HT1Z
 lapply (cpms_trans … HTZ2 … HZ02) -Z2 <arith_l4 #HT2Z
 /2 width=3 by ex2_intro/
 qed-.
+
+fact cnv_cpms_conf_lpr_aux (a) (h) (o):
+                           ∀G0,L0,T0. 𝐏[h,o]⦃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_conf_lpr a h G1 L1 T1) →
+                           ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpms_conf_lpr a h G1 L1 T1.
+#a #h #o #G #L #T #H0 #IH2 #IH1 #G0 #L0 #T0 #HG #HL #HT
+#HT0 #n1 #T1 #HT01 #n2 #T2 #HT02 #L1 #HL01 #L2 #HL02 destruct
+elim (cpms_fwd_tdpos_sn … HT0 H0 … HT01) *
+elim (cpms_fwd_tdpos_sn … HT0 H0 … HT02) *
+-H0 -HT01 -HT02
+[ #H21 #H22 #H11 #H12 destruct -a -o -L0
+  <minus_n_O 
+  /2 width=1 by cnv_cpms_conf_lpr_refl_refl_aux/
+| #m21 #m22 #X2 #HX02 #HnX02 #HXT2 #H2 #H11 #H12 destruct
+  <minus_n_O <minus_O_n
+  @(cnv_cpms_conf_lpr_refl_step_aux … IH2 IH1) -IH2 -IH1 /2 width=4 by/
+| #H21 #H22 #m11 #m12 #X1 #HX01 #HnX01 #HXT1 #H1 destruct
+  <minus_n_O <minus_O_n
+  @ex2_commute @(cnv_cpms_conf_lpr_refl_step_aux … IH2 IH1) -IH2 -IH1 /2 width=4 by/
+| #m21 #m22 #X2 #HX02 #HnX02 #HXT2 #H2 #m11 #m12 #X1 #HX01 #HnX01 #HXT1 #H1 destruct
+  @(cnv_cpms_conf_lpr_step_step_aux … IH2 IH1) -IH2 -IH1 /2 width=4 by/
+]
+qed-.