update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cnr_teqx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_teqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_teqx.ma
index 0f2f9d709d36979e5c8df2f35a69323fc937d397..f516a4ef1bc441cf28f0909b8612e33d81c38113 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_teqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_teqx.ma
@@ -12,10 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/relocation/lifts_teqx.ma".
-include "basic_2/rt_transition/cpr_drops_basic.ma".
-include "basic_2/rt_transition/cnr_simple.ma".
-include "basic_2/rt_transition/cnr_drops.ma".
+include "static_2/syntax/teqx.ma".
+include "basic_2/rt_transition/cnr_teqg.ma".
 
 (* NORMAL TERMS FOR CONTEXT-SENSITIVE R-TRANSITION **************************)
 
@@ -25,73 +23,5 @@ include "basic_2/rt_transition/cnr_drops.ma".
 (* Basic_2A1: uses: cnr_dec *)
 lemma cnr_dec_teqx (h) (G) (L):
       ∀T1. ∨∨ ❪G,L❫ ⊢ ➡𝐍[h,0] T1
-            | ∃∃T2. ❪G,L❫ ⊢ T1 ➡[h,0] T2 & (T1 ≛ T2 → ⊥).
-#h #G #L #T1
-@(fqup_wf_ind_eq (Ⓣ) … G L T1) -G -L -T1 #G0 #L0 #T0 #IH #G #L * *
-[ #s #HG #HL #HT destruct -IH
-  /3 width=4 by cnr_sort, or_introl/
-| #i #HG #HL #HT destruct -IH
-  elim (drops_F_uni L i)
-  [ /3 width=6 by cnr_lref_atom, or_introl/
-  | * * [ #I | * #V ] #K #HLK
-    [ /3 width=7 by cnr_lref_unit, or_introl/
-    | elim (lifts_total V 𝐔❨↑i❩) #W #HVW
-      @or_intror @(ex2_intro … W) [ /2 width=6 by cpm_delta_drops/ ] #H
-      lapply (teqx_inv_lref1 … H) -H #H destruct
-      /2 width=5 by lifts_inv_lref2_uni_lt/
-    | /3 width=7 by cnr_lref_abst, or_introl/
-    ]
-  ]
-| #l #HG #HL #HT destruct -IH
-  /3 width=4 by cnr_gref, or_introl/
-| #p * [ cases p ] #V1 #T1 #HG #HL #HT destruct
-  [ elim (cpr_subst h G (L.ⓓV1) T1 0 L V1) [| /2 width=1 by drops_refl/ ] #T2 #X2 #HT12 #HXT2 -IH
-    elim (teqx_dec T1 T2) [ -HT12 #HT12 | #HnT12 ]
-    [ elim (teqx_inv_lifts_dx … HT12 … HXT2) -T2 #X1 #HXT1 #_ -X2
-      @or_intror @(ex2_intro … X1) [ /2 width=3 by cpm_zeta/ ] #H
-      /2 width=7 by teqx_lifts_inv_pair_sn/
-    | @or_intror @(ex2_intro … (+ⓓV1.T2)) [ /2 width=1 by cpm_bind/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    ]
-  | elim (IH G L V1) [ elim (IH G (L.ⓓV1) T1) [| * | // ] | * | // ] -IH
-    [ #HT1 #HV1 /3 width=6 by cnr_abbr_neg, or_introl/
-    | #T2 #HT12 #HnT12 #_
-      @or_intror @(ex2_intro … (-ⓓV1.T2)) [ /2 width=1 by cpm_bind/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    | #V2 #HV12 #HnV12
-      @or_intror @(ex2_intro … (-ⓓV2.T1)) [ /2 width=1 by cpr_pair_sn/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    ]
-  | elim (IH G L V1) [ elim (IH G (L.ⓛV1) T1) [| * | // ] | * | // ] -IH
-    [ #HT1 #HV1 /3 width=6 by cnr_abst, or_introl/
-    | #T2 #HT12 #HnT12 #_
-      @or_intror @(ex2_intro … (ⓛ[p]V1.T2)) [ /2 width=1 by cpm_bind/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    | #V2 #HV12 #HnV12
-      @or_intror @(ex2_intro … (ⓛ[p]V2.T1)) [ /2 width=1 by cpr_pair_sn/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    ]
-  ]
-| * #V1 #T1 #HG #HL #HT destruct [| -IH ]
-  [ elim (IH G L V1) [ elim (IH G L T1) [| * | // ] | * | // ] -IH
-    [ #HT1 #HV1
-      elim (simple_dec_ex T1) [| * #p * #W1 #U1 #H destruct ]
-      [ /3 width=6 by cnr_appl_simple, or_introl/
-      | elim (lifts_total V1 𝐔❨1❩) #X1 #HVX1
-        @or_intror @(ex2_intro … (ⓓ[p]W1.ⓐX1.U1)) [ /2 width=3 by cpm_theta/ ] #H
-        elim (teqx_inv_pair … H) -H #H destruct
-      | @or_intror @(ex2_intro … (ⓓ[p]ⓝW1.V1.U1)) [ /2 width=1 by cpm_beta/ ] #H
-        elim (teqx_inv_pair … H) -H #H destruct
-      ]
-    | #T2 #HT12 #HnT12 #_
-      @or_intror @(ex2_intro … (ⓐV1.T2)) [ /2 width=1 by cpm_appl/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    | #V2 #HV12 #HnV12
-      @or_intror @(ex2_intro … (ⓐV2.T1)) [ /2 width=1 by cpr_pair_sn/ ] #H
-      elim (teqx_inv_pair … H) -H /2 width=1 by/
-    ]
-  | @or_intror @(ex2_intro … T1) [ /2 width=1 by cpm_eps/ ] #H
-    /2 width=4 by teqx_inv_pair_xy_y/
-  ]
-]
-qed-.
+            | ∃∃T2. ❪G,L❫ ⊢ T1 ➡[h,0] T2 & (T1 ≅ T2 → ⊥).
+/2 width=1 by cnr_dec_teqg/ qed-.