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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
index b10b13a28999b03cdba2ca9f8f805f4e8d62b672..bd4e16df9444deb3064a9c9a2972bb1ccbd525bf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
@@ -19,47 +19,47 @@ include "basic_2/reduction/cpx.ma".
 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
 
 definition lpx: ∀h. sd h → relation3 genv lenv lenv ≝
-                λh,g,G. lpx_sn (cpx h g G).
+                λh,o,G. lpx_sn (cpx h o G).
 
 interpretation "extended parallel reduction (local environment, sn variant)"
-   'PRedSn h g G L1 L2 = (lpx h g G L1 L2).
+   'PRedSn h o G L1 L2 = (lpx h o G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lpx_inv_atom1: ∀h,g,G,L2. ⦃G, ⋆⦄ ⊢ ➡[h, g] L2 → L2 = ⋆.
+lemma lpx_inv_atom1: ∀h,o,G,L2. ⦃G, ⋆⦄ ⊢ ➡[h, o] L2 → L2 = ⋆.
 /2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
 
-lemma lpx_inv_pair1: ∀h,g,I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, g] L2 →
-                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, g] V2 &
+lemma lpx_inv_pair1: ∀h,o,I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, o] L2 →
+                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡[h, o] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, o] V2 &
                               L2 = K2. ⓑ{I} V2.
 /2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
 
-lemma lpx_inv_atom2: ∀h,g,G,L1.  ⦃G, L1⦄ ⊢ ➡[h, g] ⋆ → L1 = ⋆.
+lemma lpx_inv_atom2: ∀h,o,G,L1.  ⦃G, L1⦄ ⊢ ➡[h, o] ⋆ → L1 = ⋆.
 /2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
 
-lemma lpx_inv_pair2: ∀h,g,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ➡[h, g] K2.ⓑ{I}V2 →
-                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, g] V2 &
+lemma lpx_inv_pair2: ∀h,o,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ➡[h, o] K2.ⓑ{I}V2 →
+                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡[h, o] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, o] V2 &
                              L1 = K1. ⓑ{I} V1.
 /2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
 
-lemma lpx_inv_pair: ∀h,g,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ➡[h, g] L2.ⓑ{I2}V2 →
-                    ∧∧ ⦃G, L1⦄ ⊢ ➡[h, g] L2 & ⦃G, L1⦄ ⊢ V1 ➡[h, g] V2 & I1 = I2.
+lemma lpx_inv_pair: ∀h,o,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ➡[h, o] L2.ⓑ{I2}V2 →
+                    ∧∧ ⦃G, L1⦄ ⊢ ➡[h, o] L2 & ⦃G, L1⦄ ⊢ V1 ➡[h, o] V2 & I1 = I2.
 /2 width=1 by lpx_sn_inv_pair/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lpx_refl: ∀h,g,G,L.  ⦃G, L⦄ ⊢ ➡[h, g] L.
+lemma lpx_refl: ∀h,o,G,L.  ⦃G, L⦄ ⊢ ➡[h, o] L.
 /2 width=1 by lpx_sn_refl/ qed.
 
-lemma lpx_pair: ∀h,g,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 → ⦃G, K1⦄ ⊢ V1 ➡[h, g] V2 →
-                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, g] K2.ⓑ{I}V2.
+lemma lpx_pair: ∀h,o,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡[h, o] K2 → ⦃G, K1⦄ ⊢ V1 ➡[h, o] V2 →
+                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, o] K2.ⓑ{I}V2.
 /2 width=1 by lpx_sn_pair/ qed.
 
-lemma lpr_lpx: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡[h, g] L2.
-#h #g #G #L1 #L2 #H elim H -L1 -L2 /3 width=1 by lpx_pair, cpr_cpx/
+lemma lpr_lpx: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡[h, o] L2.
+#h #o #G #L1 #L2 #H elim H -L1 -L2 /3 width=1 by lpx_pair, cpr_cpx/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lpx_fwd_length: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → |L1| = |L2|.
+lemma lpx_fwd_length: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → |L1| = |L2|.
 /2 width=2 by lpx_sn_fwd_length/ qed-.