component "unfold" updated to new syntax ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / tpss_ltps.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma
index abaf3f7c0df318a5c376bf7740ea847101a7da65..18b181741955bc3c94b3082b69847ae7c082fb0b 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma
@@ -24,16 +24,16 @@ lemma ltps_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2.
                          L0 ⊢ T2 [d2, e2] ≫* U2 → L1 ⊢ T2 [d2, e2] ≫* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HL01 #H @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU
-lapply (ltps_tps_conf_ge … HU2 … HL01 ?) -HU2 HL01 /2/
+lapply (ltps_tps_conf_ge … HU2 … HL01 ?) -HU2 -HL01 // /2 width=3/
 qed.
 
 lemma ltps_tpss_conf: ∀L0,L1,T2,U2,d1,e1,d2,e2.
                       L0 [d1, e1] ≫ L1 → L0 ⊢ T2 [d2, e2] ≫* U2 →
                       ∃∃T. L1 ⊢ T2 [d2, e2] ≫* T & L1 ⊢ U2 [d1, e1] ≫* T.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #HL01 #H @(tpss_ind … H) -U2
-[ /3/
+[ /3 width=3/
 | #U #U2 #_ #HU2 * #T #HT2 #HUT
-  elim (ltps_tps_conf … HU2 … HL01) -HU2 HL01 #W #HUW #HU2W
+  elim (ltps_tps_conf … HU2 … HL01) -HU2 -HL01 #W #HUW #HU2W
   elim (tpss_strip_eq … HUT … HUW) -U
   /3 width=5 by ex2_1_intro, step, tpss_strap/ (**) (* just /3 width=5/ is too slow *)
 ]
@@ -44,42 +44,43 @@ lemma ltps_tpss_trans_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2.
                           L0 ⊢ T2 [d2, e2] ≫* U2 → L1 ⊢ T2 [d2, e2] ≫* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HL10 #H @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU
-lapply (ltps_tps_trans_ge … HU2 … HL10 ?) -HU2 HL10 /2/
+lapply (ltps_tps_trans_ge … HU2 … HL10 ?) -HU2 -HL10 // /2 width=3/
 qed.
 
 lemma ltps_tpss_trans_down: ∀L0,L1,T2,U2,d1,e1,d2,e2. d2 + e2 ≤ d1 →
                             L1 [d1, e1] ≫ L0 → L0 ⊢ T2 [d2, e2] ≫* U2 →
                             ∃∃T. L1 ⊢ T2 [d2, e2] ≫* T & L0 ⊢ T [d1, e1] ≫* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde2d1 #HL10 #H @(tpss_ind … H) -U2
-[ /3/
+[ /3 width=3/
 | #U #U2 #_ #HU2 * #T #HT2 #HTU
   elim (tpss_strap1_down … HTU … HU2 ?) -U // #U #HTU #HU2
-  elim (ltps_tps_trans … HTU … HL10) -HTU HL10 #W #HTW #HWU
-  @(ex2_1_intro … W) /2/ (**) (* /3 width=5/ does not work as in ltps_tpss_conf *)
+  elim (ltps_tps_trans … HTU … HL10) -HTU -HL10 #W #HTW #HWU
+  @(ex2_1_intro … W) /2 width=3/ (**) (* /3 width=5/ does not work as in ltps_tpss_conf *)
 ]
 qed.
 
 fact ltps_tps_trans_eq_aux: ∀Y1,X2,L1,T2,U2,d,e.
                             L1 ⊢ T2 [d, e] ≫ U2 → ∀L0. L0 [d, e] ≫ L1 →
                             Y1 = L1 → X2 = T2 → L0 ⊢ T2 [d, e] ≫* U2.
-#Y1 #X2 @(cw_wf_ind … Y1 X2) -Y1 X2 #Y1 #X2 #IH
-#L1 #T2 #U2 #d #e * -L1 T2 U2 d e
+#Y1 #X2 @(cw_wf_ind … Y1 X2) -Y1 -X2 #Y1 #X2 #IH
+#L1 #T2 #U2 #d #e * -L1 -T2 -U2 -d -e
 [ //
-| #L1 #K1 #V1 #W1 #i #d #e #Hdi #Hide #HLK1 #HVW1 #L0 #HL10 #H1 #H2 destruct -Y1 X2;
+| #L1 #K1 #V1 #W1 #i #d #e #Hdi #Hide #HLK1 #HVW1 #L0 #HL10 #H1 #H2 destruct
   lapply (ldrop_fwd_lw … HLK1) normalize #H1
-  elim (ltps_ldrop_trans_be … HL10 … HLK1 ? ?) -HL10 HLK1 [2,3: /2/ ] #X #H #HLK0
-  elim (ltps_inv_tps22 … H ?) -H [2: /2/ ] #K0 #V0 #HK01 #HV01 #H destruct -X;
+  elim (ltps_ldrop_trans_be … HL10 … HLK1 ? ?) -HL10 -HLK1 /2 width=1/ #X #H #HLK0
+  elim (ltps_inv_tps22 … H ?) -H /2 width=1/ #K0 #V0 #HK01 #HV01 #H destruct
   lapply (tps_fwd_tw … HV01) #H2
-  lapply (transitive_le (#[K1] + #[V0]) … H1) -H1 [ /2/ ] -H2 #H
-  lapply (IH … HV01 … HK01 ? ?) -IH HV01 HK01 [1,3: // |2,4: skip | normalize /2/ | /3 width=6/ ]
-| #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #L0 #HL0 #H1 #H2 destruct -Y1 X2;
-  lapply (tps_lsubs_conf … HT12 (L. 𝕓{I} V1) ?) -HT12 /2/ #HT12
+  lapply (transitive_le (#[K1] + #[V0]) … H1) -H1 /2 width=1/ -H2 #H
+  lapply (IH … HV01 … HK01 ? ?) -IH -HV01 -HK01
+  [1,3: // |2,4: skip | normalize /2 width=1/ | /3 width=6/ ]
+| #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #L0 #HL0 #H1 #H2 destruct
+  lapply (tps_lsubs_conf … HT12 (L. 𝕓{I} V1) ?) -HT12 /2 width=1/ #HT12
   lapply (IH … HV12 … HL0 ? ?) -HV12 [1,3,5: normalize // |2,4: skip ] #HV12
-  lapply (IH … HT12 (L0. 𝕓{I} V1) ? ? ?) -IH HT12 [1,3,5: /2/ |2,4: skip | normalize // ] -HL0 #HT12
-  lapply (tpss_lsubs_conf … HT12 (L0. 𝕓{I} V2) ?) -HT12 /2/
-| #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #L0 #HL0 #H1 #H2 destruct -Y1 X2;
+  lapply (IH … HT12 (L0. 𝕓{I} V1) ? ? ?) -IH -HT12 [1,3,5: /2 width=2/ |2,4: skip | normalize // ] -HL0 #HT12
+  lapply (tpss_lsubs_conf … HT12 (L0. 𝕓{I} V2) ?) -HT12 /2 width=1/
+| #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #L0 #HL0 #H1 #H2 destruct
   lapply (IH … HV12 … HL0 ? ?) -HV12 [1,3,5: normalize // |2,4: skip ]
-  lapply (IH … HT12 … HL0 ? ?) -IH HT12 [1,3,5: normalize // |2,4: skip ] -HL0 /2/
+  lapply (IH … HT12 … HL0 ? ?) -IH -HT12 [1,3,5: normalize // |2,4: skip ] -HL0 /2 width=1/
 ]
 qed.
 
@@ -90,5 +91,5 @@ lemma ltps_tps_trans_eq: ∀L1,T2,U2,d,e. L1 ⊢ T2 [d, e] ≫ U2 →
 lemma ltps_tpss_trans_eq: ∀L0,L1,T2,U2,d,e. L0 [d, e] ≫ L1 →
                           L1 ⊢ T2 [d, e] ≫* U2 → L0 ⊢ T2 [d, e] ≫* U2.
 #L0 #L1 #T2 #U2 #d #e #HL01 #H @(tpss_ind … H) -U2 //
-#U #U2 #_ #HU2 #IHU @(tpss_trans_eq … IHU) /2/
+#U #U2 #_ #HU2 #IHU @(tpss_trans_eq … IHU) /2 width=3/
 qed.