- name changes in the rediction rules

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
index 45e71b66ee59ecee9d01d34ac3468e7be982f0d0..1cd6da260aecdc8cc0996f363f78e78d632a19d0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
@@ -24,7 +24,7 @@ include "basic_2/reduction/cpx.ma".
 lemma ssta_cpx: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •[h, g] T2 →
                 ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
 #h #g #G #L #T1 #T2 #l #H elim H -G -L -T1 -T2
-[ /3 width=4 by cpx_sort, da_inv_sort/
+[ /3 width=4 by cpx_st, da_inv_sort/
 | #G #L #K #V #U #W #i #HLK #_ #HWU #IHVW #H
   elim (da_inv_lref … H) -H * #K0 #V0 [| #l0 ] #HLK0
   lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpx_delta/
@@ -33,7 +33,7 @@ lemma ssta_cpx: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •[h, g] T2 →
   lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct /2 width=7 by cpx_delta/
 | /4 width=2 by cpx_bind, da_inv_bind/
 | /4 width=3 by cpx_flat, da_inv_flat/
-| /4 width=3 by cpx_tau, da_inv_flat/
+| /4 width=3 by cpx_eps, da_inv_flat/
 ]
 qed.
 
@@ -45,7 +45,7 @@ lemma cpx_lift: ∀h,g,G. l_liftable (cpx h g G).
   >(lift_mono … H1 … H2) -H1 -H2 //
 | #G #K #k #l #Hkl #L #s #d #e #_ #U1 #H1 #U2 #H2
   >(lift_inv_sort1 … H1) -U1
-  >(lift_inv_sort1 … H2) -U2 /2 width=2 by cpx_sort/
+  >(lift_inv_sort1 … H2) -U2 /2 width=2 by cpx_st/
 | #I #G #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #s #d #e #HLK #U1 #H #U2 #HWU2
   elim (lift_inv_lref1 … H) * #Hid #H destruct
   [ elim (lift_trans_ge … HVW2 … HWU2) -W2 // <minus_plus #W2 #HVW2 #HWU2
@@ -65,9 +65,9 @@ lemma cpx_lift: ∀h,g,G. l_liftable (cpx h g G).
   elim (lift_inv_bind1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
   elim (lift_conf_O1 … HTU2 … HT2) -T2 /4 width=6 by cpx_zeta, ldrop_skip/
 | #G #K #V #T1 #T2 #_ #IHT12 #L #s #d #e #HLK #U1 #H #U2 #HTU2
-  elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=6 by cpx_tau/
+  elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=6 by cpx_eps/
 | #G #K #V1 #V2 #T #_ #IHV12 #L #s #d #e #HLK #U1 #H #U2 #HVU2
-  elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=6 by cpx_ti/
+  elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=6 by cpx_ct/
 | #a #G #K #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #s #d #e #HLK #X1 #HX1 #X2 #HX2
   elim (lift_inv_flat1 … HX1) -HX1 #V0 #X #HV10 #HX #HX1 destruct
   elim (lift_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT10 #HX destruct
@@ -90,7 +90,7 @@ lemma cpx_inv_lift1: ∀h,g,G. l_deliftable_sn (cpx h g G).
   | lapply (lift_inv_gref2 … H) -H #H destruct /2 width=3 by cpx_atom, lift_gref, ex2_intro/
   ]
 | #G #L #k #l #Hkl #K #s #d #e #_ #T1 #H
-  lapply (lift_inv_sort2 … H) -H #H destruct /3 width=3 by cpx_sort, lift_sort, ex2_intro/
+  lapply (lift_inv_sort2 … H) -H #H destruct /3 width=3 by cpx_st, lift_sort, ex2_intro/
 | #I #G #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #s #d #e #HLK #T1 #H
   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
   [ elim (ldrop_conf_lt … HLK … HLV) -L // #L #U #HKL #HLV #HUV
@@ -115,10 +115,10 @@ lemma cpx_inv_lift1: ∀h,g,G. l_deliftable_sn (cpx h g G).
   elim (lift_div_le … HU2 … HTU) -U /3 width=5 by cpx_zeta, ex2_intro/
 | #G #L #V #U1 #U2 #_ #IHU12 #K #s #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
-  elim (IHU12 … HLK … HTU1) -L -U1 /3 width=3 by cpx_tau, ex2_intro/
+  elim (IHU12 … HLK … HTU1) -L -U1 /3 width=3 by cpx_eps, ex2_intro/
 | #G #L #V1 #V2 #U1 #_ #IHV12 #K #s #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
-  elim (IHV12 … HLK … HWV1) -L -V1 /3 width=3 by cpx_ti, ex2_intro/
+  elim (IHV12 … HLK … HWV1) -L -V1 /3 width=3 by cpx_ct, ex2_intro/
 | #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #K #s #d #e #HLK #X #HX
   elim (lift_inv_flat2 … HX) -HX #V0 #Y #HV01 #HY #HX destruct
   elim (lift_inv_bind2 … HY) -HY #W0 #T0 #HW01 #HT01 #HY destruct
@@ -139,9 +139,9 @@ qed-.
 
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 ⦃G2, L2, T2⦄ →
+lemma fqu_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 ⦃G2, L2, T2⦄ →
                      ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
-                     â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\83 ⦃G2, L2, U2⦄.
+                     â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\90 ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 
 /3 width=3 by fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, cpx_pair_sn, cpx_bind, cpx_flat, ex2_intro/
 [ #I #G #L #V2 #U2 #HVU2
@@ -153,30 +153,30 @@ lemma fqu_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T
 ]
 qed-.
 
-lemma fqu_ssta_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 ⦃G2, L2, T2⦄ →
+lemma fqu_ssta_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 •[h, g] U2 →
                       ∀l. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] l+1 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\83 ⦃G2, L2, U2⦄.
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\90 ⦃G2, L2, U2⦄.
 /3 width=5 by fqu_cpx_trans, ssta_cpx/ qed-.
 
-lemma fquq_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\83⸮ ⦃G2, L2, U2⦄.
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\90⸮ ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H
 [ #HT12 elim (fqu_cpx_trans … HT12 … HTU2) /3 width=3 by fqu_fquq, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fquq_ssta_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_ssta_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ →
                        ∀U2. ⦃G2, L2⦄ ⊢ T2 •[h, g] U2 →
                        ∀l. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] l+1 →
-                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\83⸮ ⦃G2, L2, U2⦄.
+                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\90⸮ ⦃G2, L2, U2⦄.
 /3 width=5 by fquq_cpx_trans, ssta_cpx/ qed-.
 
-lemma fqup_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ →
+lemma fqup_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\83+ ⦃G2, L2, U2⦄.
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\90+ ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 [ #G2 #L2 #T2 #H12 #U2 #HTU2 elim (fqu_cpx_trans … H12 … HTU2) -T2
   /3 width=3 by fqu_fqup, ex2_intro/
@@ -186,18 +186,18 @@ lemma fqup_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2,
 ]
 qed-.
 
-lemma fqus_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83* ⦃G2, L2, T2⦄ →
+lemma fqus_cpx_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90* ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\83* ⦃G2, L2, U2⦄.
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & â¦\83G1, L1, U1â¦\84 â\8a\90* ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fqus_inv_gen … H) -H
 [ #HT12 elim (fqup_cpx_trans … HT12 … HTU2) /3 width=3 by fqup_fqus, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fqu_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 ⦃G2, L2, T2⦄ →
+lemma fqu_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 ⦃G2, L2, T2⦄ →
                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 → (T2 = U2 → ⊥) →
-                         â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\83 ⦃G2, L2, U2⦄.
+                         â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\90 ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lift_total V2 0 1)
   #U2 #HVU2 @(ex3_intro … U2)
@@ -223,9 +223,9 @@ lemma fqu_cpx_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L
 ]
 qed-.
 
-lemma fquq_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ →
                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\83⸮ ⦃G2, L2, U2⦄.
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\90⸮ ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fquq_inv_gen … H12) -H12
 [ #H12 elim (fqu_cpx_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -233,9 +233,9 @@ lemma fquq_cpx_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G
 ]
 qed-.
 
-lemma fqup_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ →
+lemma fqup_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ →
                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\83+ ⦃G2, L2, U2⦄.
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\90+ ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
 [ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpx_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -245,9 +245,9 @@ lemma fqup_cpx_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2,
 ]
 qed-.
 
-lemma fqus_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83* ⦃G2, L2, T2⦄ →
+lemma fqus_cpx_trans_neq: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90* ⦃G2, L2, T2⦄ →
                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\83* ⦃G2, L2, U2⦄.
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, g] U1 & T1 = U1 â\86\92 â\8a¥ & â¦\83G1, L1, U1â¦\84 â\8a\90* ⦃G2, L2, U2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_gen … H12) -H12
 [ #H12 elim (fqup_cpx_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/