renaming

[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 5b27cd1a990202cbe587809ff6d2377efdb66f12..43eb814dc017629381af95a5c8a8bc960e238239 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
@@ -27,42 +27,42 @@ theorem aaa_fsb: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ≥[h, o] 𝐒⦃G,
 
 (* Advanced eliminators with atomic arity assignment for terms **************)
 
-fact aaa_ind_fpb_aux: ∀h,o. ∀R:relation3 ….
+fact aaa_ind_fpb_aux: ∀h,o. ∀Q:relation3 ….
                       (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                    (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                    R G1 L1 T1
+                                    (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                                    Q G1 L1 T1
                       ) →
-                      ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+                      ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ∀A. ⦃G, L⦄ ⊢ T ⁝ A →  Q G L T.
 #h #o #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 h o … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpb_fpbs/
 qed-.
 
-lemma aaa_ind_fpb: ∀h,o. ∀R:relation3 ….
+lemma aaa_ind_fpb: ∀h,o. ∀Q:relation3 ….
                    (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                 R G1 L1 T1
+                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                                 Q G1 L1 T1
                    ) →
-                   ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R 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,o. ∀R:relation3 ….
+fact aaa_ind_fpbg_aux: ∀h,o. ∀Q:relation3 ….
                        (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                     R G1 L1 T1
+                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                                     Q G1 L1 T1
                        ) →
-                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
+                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ∀A. ⦃G, L⦄ ⊢ T ⁝ A →  Q G L T.
+#h #o #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 h o … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpbg_fwd_fpbs/
 qed-.
 
-lemma aaa_ind_fpbg: ∀h,o. ∀R:relation3 ….
+lemma aaa_ind_fpbg: ∀h,o. ∀Q:relation3 ….
                     (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                  R G1 L1 T1
+                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                                  Q G1 L1 T1
                     ) →
-                    ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R 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-.