- new component "s_transition" for the restored fqu and fquq

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / fpbq_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma
index 8bc5c210de546e37682b9984fa7a0300aefc35bd..2a6cf508730efa28aca27058a633871aa93a2644 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma
@@ -20,32 +20,32 @@ include "basic_2/reduction/fpbq.ma".
 
 (* alternative definition of fpbq *)
 definition fpbqa: ∀h. sd h → tri_relation genv lenv term ≝
-                  λh,g,G1,L1,T1,G2,L2,T2.
-                  ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄.
+                  λh,o,G1,L1,T1,G2,L2,T2.
+                  ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄.
 
 interpretation
    "'qrst' parallel reduction (closure) alternative"
-   'BTPRedAlt h g G1 L1 T1 G2 L2 T2 = (fpbqa h g G1 L1 T1 G2 L2 T2).
+   'BTPRedAlt h o G1 L1 T1 G2 L2 T2 = (fpbqa h o G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fleq_fpbq: ∀h,g,G1,G2,L1,L2,T1,T2.
-                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by fpbq_lleq/
+lemma fleq_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2.
+                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by fpbq_lleq/
 qed.
 
-lemma fpb_fpbq: ∀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 * -G2 -L2 -T2
+lemma fpb_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
+                ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
 /3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/
 qed.
 
 (* Main properties **********************************************************)
 
-theorem fpbq_fpbqa: ∀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 * -G2 -L2 -T2
+theorem fpbq_fpbqa: ∀h,o,G1,G2,L1,L2,T1,T2.
+                    ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ≽≽[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
 [ #G2 #L2 #T2 #H elim (fquq_inv_gen … H) -H
   [ /3 width=1 by fpb_fqu, or_intror/
   | * #H1 #H2 #H3 destruct /2 width=1 by or_introl/
@@ -58,29 +58,29 @@ theorem fpbq_fpbqa: ∀h,g,G1,G2,L1,L2,T1,T2.
 ]
 qed.
 
-theorem fpbqa_inv_fpbq: ∀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 * /2 width=1 by fleq_fpbq, fpb_fpbq/
+theorem fpbqa_inv_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2.
+                        ⦃G1, L1, T1⦄ ≽≽[h, o] ⦃G2, L2, T2⦄ →
+                        ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by fleq_fpbq, fpb_fpbq/
 qed-.
 
 (* Advanced eliminators *****************************************************)
 
-lemma fpbq_ind_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ∀R:Prop.
+lemma fpbq_ind_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ∀R:Prop.
                     (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → R) →
-                    (⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R) →
-                    ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ → R.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #R #HI1 #HI2 #H elim (fpbq_fpbqa … H) /2 width=1 by/
+                    (⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R) →
+                    ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → R.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #R #HI1 #HI2 #H elim (fpbq_fpbqa … H) /2 width=1 by/
 qed-.
 
 (* aternative definition of fpb *********************************************)
 
-lemma fpb_fpbq_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
-                    ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ ∧ (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥).
+lemma fpb_fpbq_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ ∧ (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥).
 /3 width=10 by fpb_fpbq, fpb_inv_fleq, conj/ qed.
 
-lemma fpbq_inv_fpb_alt: ∀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 #H0 @(fpbq_ind_alt … H) -H //
+lemma fpbq_inv_fpb_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
+                        (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥) → ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #H0 @(fpbq_ind_alt … H) -H //
 #H elim H0 -H0 //
 qed-.