milestone update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fsb_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma
index b95c6ced6f27940cee4ca3a022484537d759e059..4da3d3d9f723176748e7437f2e3f79158b345431 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma
@@ -14,54 +14,58 @@
 
 include "basic_2/rt_computation/csx_aaa.ma".
 include "basic_2/rt_computation/fpbs_aaa.ma".
-include "basic_2/rt_computation/fpbs_fpb.ma".
 include "basic_2/rt_computation/fsb_csx.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
 (* Main properties with atomic arity assignment for terms *******************)
 
-theorem aaa_fsb: ∀h,G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ≥[h] 𝐒⦃G,L,T⦄.
+theorem aaa_fsb (G) (L) (T) (A):
+        ❪G,L❫ ⊢ T ⁝ A → ≥𝐒 ❪G,L,T❫.
 /3 width=2 by aaa_csx, csx_fsb/ qed.
 
 (* Advanced eliminators with atomic arity assignment for terms **************)
 
-fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
-                      (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
-                                    (∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                                    Q G1 L1 T1
-                      ) →
-                      ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ∀A. ⦃G,L⦄ ⊢ T ⁝ A →  Q G L T.
-#h #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
+fact aaa_ind_fpbc_aux (Q:relation3 …):
+     (∀G1,L1,T1,A.
+       ❪G1,L1❫ ⊢ T1 ⁝ A →
+       (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+       Q G1 L1 T1
+     ) →
+     ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A →  Q G L T.
+#R #IH #G #L #T #H @(csx_ind_fpbc … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
-/2 width=2 by fpb_fpbs/
+/2 width=2 by fpbc_fpbs/
 qed-.
 
-lemma aaa_ind_fpb: ∀h. ∀Q:relation3 ….
-                   (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
-                                 (∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                                 Q G1 L1 T1
-                   ) →
-                   ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
-/4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
+lemma aaa_ind_fpbc (Q:relation3 …):
+      (∀G1,L1,T1,A.
+        ❪G1,L1❫ ⊢ T1 ⁝ A →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
+/4 width=4 by aaa_ind_fpbc_aux, aaa_csx/ qed-.
 
-fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
-                       (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
-                                     (∀G2,L2,T2. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                                     Q G1 L1 T1
-                       ) →
-                       ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ∀A. ⦃G,L⦄ ⊢ T ⁝ A →  Q G L T.
-#h #Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
+fact aaa_ind_fpbg_aux (Q:relation3 …):
+     (∀G1,L1,T1,A.
+       ❪G1,L1❫ ⊢ T1 ⁝ A →
+       (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+       Q G1 L1 T1
+     ) →
+     ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A →  Q G L T.
+#Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpbg_fwd_fpbs/
 qed-.
 
-lemma aaa_ind_fpbg: ∀h. ∀Q:relation3 ….
-                    (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
-                                  (∀G2,L2,T2. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                                  Q G1 L1 T1
-                    ) →
-                    ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
+lemma aaa_ind_fpbg (Q:relation3 …):
+      (∀G1,L1,T1,A.
+        ❪G1,L1❫ ⊢ T1 ⁝ A →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.