X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Ffpbg_fpbs.ma;h=b5a303df6d4908bd9fa22eed973b146e3eb79f99;hb=9afdb35b870c15760f482a1b4a0ad7b4dcd5172b;hp=4b866229537002e36ce3c8455843df33c0654959;hpb=6f1f9e20aa2775d41bba64289fc903e6612baaf3;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbs.ma
index 4b8662295..b5a303df6 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbs.ma
@@ -20,47 +20,41 @@ include "basic_2/computation/fpbg_fleq.ma".
 
 (* Properties on "qrst" parallel reduction on closures **********************)
 
-lemma fpbg_fpb_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
-                      ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fpb_fpbu … H2) -H2
-/3 width=5 by fpbg_fleq_trans, fpbg_strap1, fpbu_fpbc/
-qed-.
-
 lemma fpb_fpbg_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
+                      ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
                       ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 elim (fpb_fpbu … H1) -H1
-/3 width=5 by fleq_fpbg_trans, fpbg_strap2, fpbu_fpbc/
+/3 width=5 by fpbg_fwd_fpbs, ex2_3_intro/ qed-.
+
+lemma fpbq_fpbg_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
+                       ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
+                       ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fpbq_ind_alt … H1) -H1
+/2 width=5 by fleq_fpbg_trans, fpb_fpbg_trans/
 qed-.
 
 (* Properties on "qrst" parallel compuutation on closures *******************)
 
 lemma fpbs_fpbg_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
                        ∀G2,L2,T2. ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpb_fpbg_trans/
+#h #g #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
 qed-.
 
 (* Note: this is used in the closure proof *)
 lemma fpbg_fpbs_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
                        ∀G1,L1,T1. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpb_trans/
+#h #g #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
 qed-.
 
-lemma fpbu_fpbs_fpbg: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ → 
-                      ∀G2,L2,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbg_fpbs_trans, fpbu_fpbg/ qed.
-
 (* Note: this is used in the closure proof *)
 lemma fqup_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqup_inv_step_sn … H) -H
-/3 width=5 by fqus_fpbs, fpbu_fqu, fpbu_fpbs_fpbg/
+/3 width=5 by fqus_fpbs, fpb_fqu, ex2_3_intro/
 qed.
 
 lemma cpxs_fpbg: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 →
                  (T1 = T2 → ⊥) → ⦃G, L, T1⦄ >≡[h, g] ⦃G, L, T2⦄.
 #h #g #G #L #T1 #T2 #H #H0 elim (cpxs_neq_inv_step_sn … H … H0) -H -H0
-/4 width=5 by cpxs_fpbs, fpbu_cpx, fpbu_fpbs_fpbg/
+/4 width=5 by cpxs_fpbs, fpb_cpx, ex2_3_intro/
 qed.
 
 lemma lstas_fpbg: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → (T1 = T2 → ⊥) →
@@ -70,19 +64,5 @@ lemma lstas_fpbg: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → (T1
 lemma lpxs_fpbg: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
                  (L1 ≡[T, 0] L2 → ⊥) → ⦃G, L1, T⦄ >≡[h, g] ⦃G, L2, T⦄.
 #h #g #G #L1 #L2 #T #H #H0 elim (lpxs_nlleq_inv_step_sn … H … H0) -H -H0
-/4 width=5 by fpbu_fpbs_fpbg, fpbu_lpx, lpxs_lleq_fpbs/
+/4 width=5 by fpb_lpx, lpxs_lleq_fpbs, ex2_3_intro/
 qed.
-
-lemma fpbs_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨
-                 ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
-[ /2 width=1 by or_introl/
-| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1 elim (fpb_fpbu … H2) -H2 #H2
-  [ /3 width=5 by fleq_trans, or_introl/
-  | /5 width=5 by fpbc_fpbg, fleq_fpbc_trans, fpbu_fpbc, or_intror/
-  | /3 width=5 by fpbg_fleq_trans, or_intror/
-  | /4 width=5 by fpbg_strap1, fpbu_fpbc, or_intror/
-  ]
-]
-qed-.