milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_tdeq.ma
index 1c5287e63b02adce8b93171e4d3326fc9174bda9..44790ef382c31941c1634b52c648de544f6dbd4b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_tdeq.ma
@@ -18,17 +18,17 @@ include "basic_2/dynamic/cnv_cpm_tdeq_trans.ma".
 
 (* Properties with restricted rt-computation for terms **********************)
 
-fact cpms_tdneq_fwd_step_sn_aux (a) (h) (n) (o) (G) (L) (T1):
-     ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G, L⦄ ⊢ T1 ![a,h] → (T1 ≛[h,o] T2 → ⊥) →
-     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
-     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr a h G0 L0 T0) →
-     ∃∃n1,n2,T0. ⦃G, L⦄ ⊢ T1 ➡[n1,h] T0 & T1 ≛[h,o] T0 → ⊥ & ⦃G, L⦄ ⊢ T0 ➡*[n2,h] T2 & n1+n2 = n.
-#a #h #n #o #G #L #T1 #T2 #H
+fact cpms_tdneq_fwd_step_sn_aux (a) (h) (n) (G) (L) (T1):
+     ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G, L⦄ ⊢ T1 ![a,h] → (T1 ≛ T2 → ⊥) →
+     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
+     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr a h G0 L0 T0) →
+     ∃∃n1,n2,T0. ⦃G, L⦄ ⊢ T1 ➡[n1,h] T0 & T1 ≛ T0 → ⊥ & ⦃G, L⦄ ⊢ T0 ➡*[n2,h] T2 & n1+n2 = n.
+#a #h #n #G #L #T1 #T2 #H
 @(cpms_ind_sn … H) -n -T1
 [ #_ #H2T2 elim H2T2 -H2T2 //
 | #n1 #n2 #T1 #T #H1T1 #H1T2 #IH #H0T1 #H2T12 #IH2 #IH1
-  elim (tdeq_dec h o T1 T) #H2T1
-  [ elim (tdeq_dec h o T T2) #H2T2
+  elim (tdeq_dec T1 T) #H2T1
+  [ elim (tdeq_dec T T2) #H2T2
     [ -IH -IH2 -IH1 -H0T1 /4 width=7 by tdeq_trans, ex4_3_intro/
     | lapply (cnv_cpm_trans_lpr_aux … IH2 IH1 … H1T1 L ?) [6:|*: // ] -H1T2 -H2T12 #H0T
       elim (IH H0T H2T2) [|*: /4 width=5 by cpm_fpbq, fpbq_fpbg_trans/ ] -IH -IH2 -H0T -H2T2 (**)
@@ -42,23 +42,23 @@ fact cpms_tdneq_fwd_step_sn_aux (a) (h) (n) (o) (G) (L) (T1):
 ]
 qed-.
 
-fact cpms_tdeq_ind_sn (a) (h) (o) (G) (L) (T2) (Q:relation2 …):
+fact cpms_tdeq_ind_sn (a) (h) (G) (L) (T2) (Q:relation2 …):
      (⦃G, L⦄ ⊢ T2 ![a,h] → Q 0 T2) →
-     (∀n1,n2,T1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → ⦃G, L⦄ ⊢ T1 ![a,h] → T1 ≛[h,o] T → ⦃G, L⦄ ⊢ T ➡*[n2,h] T2 → ⦃G, L⦄ ⊢ T ![a,h] → T ≛[h,o] T2 → Q n2 T → Q (n1+n2) T1) →
-     ∀n,T1. ⦃G, L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G, L⦄ ⊢ T1 ![a,h] → T1 ≛[h,o] T2 →
-     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
-     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr a h G0 L0 T0) → 
+     (∀n1,n2,T1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → ⦃G, L⦄ ⊢ T1 ![a,h] → T1 ≛ T → ⦃G, L⦄ ⊢ T ➡*[n2,h] T2 → ⦃G, L⦄ ⊢ T ![a,h] → T ≛ T2 → Q n2 T → Q (n1+n2) T1) →
+     ∀n,T1. ⦃G, L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G, L⦄ ⊢ T1 ![a,h] → T1 ≛ T2 →
+     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) →
+     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr a h G0 L0 T0) → 
      Q n T1.
-#a #h #o #G #L #T2 #Q #IB1 #IB2 #n #T1 #H
+#a #h #G #L #T2 #Q #IB1 #IB2 #n #T1 #H
 @(cpms_ind_sn … H) -n -T1
 [ -IB2 #H0T2 #_ #_ #_ /2 width=1 by/
 | #n1 #n2 #T1 #T #H1T1 #H1T2 #IH #H0T1 #H2T12 #IH2 #IH1 -IB1
-  elim (tdeq_dec h o T1 T) #H2T1
+  elim (tdeq_dec T1 T) #H2T1
   [ lapply (cnv_cpm_trans_lpr_aux … IH2 IH1 … H1T1 L ?) [6:|*: // ] #H0T
     lapply (tdeq_canc_sn … H2T1 … H2T12) -H2T12 #H2T2
     /6 width=7 by cpm_fpbq, fpbq_fpbg_trans/ (**)
   | -IB2 -IH -IH2 -IH1
-    elim (cnv_fpbg_refl_false … o … H0T1) -a -Q
+    elim (cnv_fpbg_refl_false … H0T1) -a -Q
     /3 width=8 by cpm_tdneq_cpm_cpms_tdeq_sym_fwd_fpbg/
   ]
 ]