universary milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpx_cix.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cix.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cix.ma
index b7a0406cb0a1fa0ab26e1762ce7442b9cb0101fd..9bb51aebce8d8ed4b194a736649072820f2fa893 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cix.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cix.ma
@@ -17,35 +17,36 @@ include "basic_2/reduction/cpx.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
 
-(* Advanced forward lemmas on context-sensitive extended irreducible terms **)
+(* Advanced forward lemmas on irreducibility ********************************)
 
-lemma cpx_fwd_cix: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 ➡[g] T2 → ⦃h, L⦄ ⊢ 𝐈[g]⦃T1⦄ → T2 = T1.
-#h #g #L #T1 #T2 #H elim H -L -T1 -T2
+lemma cpx_fwd_cix: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → ⦃G, L⦄ ⊢ ➡[h, o] 𝐈⦃T1⦄ → T2 = T1.
+#h #o #G #L #T1 #T2 #H elim H -G -L -T1 -T2
 [ //
-| #L #k #l #Hkl #H elim (cix_inv_sort … Hkl H)
-| #I #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #H
+| #G #L #s #d #Hkd #H elim (cix_inv_sort … Hkd H)
+| #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #H
   elim (cix_inv_delta … HLK) //
-| #a * #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
+| #a * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
   [ elim (cix_inv_bind … H) -H #HV1 #HT1 * #H destruct
     lapply (IHV1 … HV1) -IHV1 -HV1 #H destruct
     lapply (IHT1 … HT1) -IHT1 #H destruct //
-  | elim (cix_inv_ib2 … H) -H /2 width=1/ /3 width=2/
+  | elim (cix_inv_ib2 … H) -H /3 width=2 by or_introl, eq_f2/
   ]
-| * #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
+| * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
   [ elim (cix_inv_appl … H) -H #HV1 #HT1 #_
     >IHV1 -IHV1 // -HV1 >IHT1 -IHT1 //
-  | elim (cix_inv_ri2 … H) /2 width=1/
+  | elim (cix_inv_ri2 … H) /2 width=1 by/
   ]
-| #L #V1 #T1 #T #T2 #_ #_ #_ #H
-  elim (cix_inv_ri2 … H) /2 width=1/
-| #L #V1 #T1 #T2 #_ #_ #H
-  elim (cix_inv_ri2 … H) /2 width=1/
-| #a #L #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
+| #G #L #V1 #T1 #T #T2 #_ #_ #_ #H
+  elim (cix_inv_ri2 … H) /2 width=1 by or_introl/
+| #G #L #V1 #T1 #T2 #_ #_ #H
+  elim (cix_inv_ri2 … H) /2 width=1 by/
+| #G #L #V1 #V2 #T #_ #_ #H
+  elim (cix_inv_ri2 … H) /2 width=1 by/
+| #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #H
   elim (cix_inv_appl … H) -H #_ #_ #H
   elim (simple_inv_bind … H)
-| #a #L #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
+| #a #G #L #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
   elim (cix_inv_appl … H) -H #_ #_ #H
   elim (simple_inv_bind … H)
 ]
 qed-.
-