lambdadelta

[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 427c0a28b4a332da6c15b587f8440c7eefcb8440..30eef62624db79dddcac78c215ce82a548e83401 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
@@ -46,16 +46,19 @@ lemma cpx_lift: ∀h,g. l_liftable (cpx h g).
   elim (lift_conf_O1 … HTU2 … HT2) -T2 /4 width=5/
 | #K #V #T1 #T2 #_ #IHT12 #L #d #e #HLK #U1 #H #U2 #HTU2
   elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=5/
-| #a #K #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #X1 #HX1 #X2 #HX2
+| #K #V1 #V2 #T #_ #IHV12 #L #d #e #HLK #U1 #H #U2 #HVU2
+  elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=5/
+| #a #K #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #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
-  elim (lift_inv_bind1 … HX2) -HX2 #V3 #T3 #HV23 #HT23 #HX2 destruct /4 width=5/
+  elim (lift_inv_bind1 … HX2) -HX2 #X #T3 #HX #HT23 #HX2 destruct
+  elim (lift_inv_flat1 … HX) -HX #W3 #V3 #HW23 #HV23 #HX destruct /4 width=5/
 | #a #K #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L #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
   elim (lift_inv_bind1 … HX2) -HX2 #W3 #X #HW23 #HX #HX2 destruct
   elim (lift_inv_flat1 … HX) -HX #V3 #T3 #HV3 #HT23 #HX destruct
-  elim (lift_trans_ge … HV2 … HV3 ?) -V2 // /4 width=5/
+  elim (lift_trans_ge … HV2 … HV3) -V2 // /4 width=5/
 ]
 qed.
 
@@ -93,38 +96,53 @@ lemma cpx_inv_lift1: ∀h,g. l_deliftable_sn (cpx h g).
 | #L #V #U1 #U2 #_ #IHU12 #K #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/
-| #a #L #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #K #d #e #HLK #X #HX
+| #L #V1 #V2 #U1 #_ #IHV12 #K #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/
+| #a #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #K #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
-  elim (IHV12 … HLK … HV01) -V1
-  elim (IHT12 (K.ⓛW0) … HT01) -T1 /2 width=1/ /3 width=5/
+  elim (IHV12 … HLK … HV01) -V1 #V3 #HV32 #HV03
+  elim (IHT12 (K.ⓛW0) … HT01) -T1 /2 width=1/ #T3 #HT32 #HT03
+  elim (IHW12 … HLK … HW01) -W1 #W3 #HW32 #HW03
+  @ex2_intro [2: /3 width=2/ | skip |3: /2 width=1/ ] (**) (* /4 width=6/ is slow *) 
 | #a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #K #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
   elim (IHV1 … HLK … HV01) -V1 #V3 #HV3 #HV03
   elim (IHT12 (K.ⓓW0) … HT01) -T1 /2 width=1/ #T3 #HT32 #HT03
   elim (IHW12 … HLK … HW01) -W1 #W3 #HW32 #HW03
-  elim (lift_trans_le … HV3 … HV2 ?) -V // #V #HV3 #HV2
+  elim (lift_trans_le … HV3 … HV2) -V // #V #HV3 #HV2
   @ex2_intro [2: /3 width=2/ | skip |3: /2 width=3/ ] (**) (* /4 width=5/ is slow *)
 ]
 qed-.
 
 (* Properties on supclosure *************************************************)
 
-lemma fsup_cpx_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
-                      ∀U2. ⦃h, L2⦄ ⊢ T2 ➡[g] U2 →
-                      ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
-#h #g #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [2,3,4,5: /3 width=5/ ]
-[ #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
+lemma fsupq_cpx_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ →
+                       ∀U2. ⦃h, L2⦄ ⊢ T2 ➡[g] U2 →
+                       ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
+#h #g #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [1: /2 width=3/ |3,4,5: /3 width=3/ ]
+[ #I #L1 #V2 #U2 #HVU2
+  elim (lift_total U2 0 1) /4 width=9/
+| #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
   elim (IHT12 … HTU2) -IHT12 -HTU2 #T #HT1 #HT2
   elim (lift_total T d e) #U #HTU
   lapply (cpx_lift … HT1 … HLK1 … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
-| #I #L1 #V2 #U2 #HVU2
-  elim (lift_total U2 0 1) /4 width=9/
 ]
 qed-.
 
+lemma fsupq_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ →
+                        ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
+                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
+/3 width=4 by fsupq_cpx_trans, ssta_cpx/ qed-.
+
+lemma fsup_cpx_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
+                      ∀U2. ⦃h, L2⦄ ⊢ T2 ➡[g] U2 →
+                      ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
+/3 width=3 by fsupq_cpx_trans, fsup_fsupq/ qed-.
+
 lemma fsup_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
                        ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
-/3 width=4 by fsup_cpx_trans, ssta_cpx/ qed-.
+/3 width=4 by fsupq_ssta_trans, fsup_fsupq/ qed-.