partial commit ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / fpbg_fpbg.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
index 9022732dcacab28783c945872b5b2a4605ee434d..97846fda46c420ff2a0d961694b9be3d048b0c9c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/computation/lpxs_lpxs.ma".
 include "basic_2/computation/fpbs_alt.ma".
 include "basic_2/computation/fpbg.ma".
 
@@ -22,20 +23,26 @@ include "basic_2/computation/fpbg.ma".
 lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
                      ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
-/3 width=5 by cpxs_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
+/3 width=5 by cpxs_fqus_lpxs_fpbs, cpxs_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
 qed-.
 
-lemma fpbg_fwd_fpb_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
-                       ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+lemma fpbg_fwd_fpbc_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
+                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
-[ #L2 #T2 #HT12 #H #HL12
-  elim (cpxs_neq_inv_step_sn … HT12 H) -HT12 -H
-  /4 width=9 by fpbsa_inv_fpbs, fpbc_cpx, ex3_2_intro, ex2_3_intro/
+[ /4 width=5 by fpbc_cpxs, lpxs_fpbs, ex2_3_intro/
 | #G2 #L #L2 #T #T2 #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
-  [ -HT1 elim (fqup_inv_step_sn … HT2) -HT2
-    /4 width=9 by fpbsa_inv_fpbs, fpbc_fqu, ex3_2_intro, ex2_3_intro/
-  | elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
-    /5 width=9 by fpbsa_inv_fpbs, fpbc_cpx, fqup_fqus, ex3_2_intro, ex2_3_intro/
+  [ -HT1 /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
+  | /5 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, fqup_fqus, ex3_2_intro, ex2_3_intro/
+  ]
+| #G2 #L #L0 #L2 #T #T2 #HT1 #HT2 #HL0 #H0 #HL02 #H02
+  lapply (lpxs_trans … HL0 … HL02) #HL2
+  elim (eq_term_dec T1 T) #H destruct
+  [ -HT1 elim (fqus_inv_gen … HT2) -HT2
+    [ /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
+    | * #H1 #H2 #H3 destruct
+      /4 width=5 by fpbc_lpxs, lpxs_fpbs, ex2_3_intro/
+    ]
+  | /4 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, ex3_2_intro, ex2_3_intro/
   ]
 ]
 qed-.