some restyling ...

[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 93e9c0ec4e38dba091da5355faa2c47d242ae96f..7ea1776a0299a280012d08896c80c91b004eda6c 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
@@ -22,17 +22,17 @@ include "basic_2/rt_computation/fsb_csx.ma".
 (* Main properties with atomic arity assignment for terms *******************)
 
 (* Note: this is the "big tree" theorem *)
-theorem aaa_fsb: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ≥[h] 𝐒⦃G, L, T⦄.
+theorem aaa_fsb: ∀h,G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ≥[h] 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) →
+                      (∀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.
+                      ∀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
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
@@ -40,19 +40,19 @@ fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
 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) →
+                   (∀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.
+                   ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
 /4 width=4 by aaa_ind_fpb_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) →
+                       (∀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.
+                       ∀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
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
@@ -60,9 +60,9 @@ fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
 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) →
+                    (∀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.
+                    ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.