partial commit: "computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpds_cpds.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma
index f5b7792cd2afd1c4e42405f1f1211a6584a4e3b4..cced2a796a0af437b03136d915145a220320ab91 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma
@@ -21,31 +21,31 @@ include "basic_2/computation/cpds.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpds_cprs_trans: ∀h,g,L,T1,T,T2.
+lemma cpds_cprs_trans: ∀h,g,G,L,T1,T,T2.
                        ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #L #T1 #T #T2 * #T0 #HT10 #HT0 #HT2
+#h #g #G #L #T1 #T #T2 * #T0 #HT10 #HT0 #HT2
 lapply (cprs_trans … HT0 … HT2) -T /2 width=3/
 qed-.
 
-lemma sstas_cpds_trans: ∀h,g,L,T1,T,T2.
+lemma sstas_cpds_trans: ∀h,g,G,L,T1,T,T2.
                         ⦃G, L⦄ ⊢ T1 •*[h, g] T → ⦃G, L⦄ ⊢ T •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #L #T1 #T #T2 #HT1 * #T0 #HT0 #HT02
+#h #g #G #L #T1 #T #T2 #HT1 * #T0 #HT0 #HT02
 lapply (sstas_trans … HT1 … HT0) -T /2 width=3/
 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpds_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{a}V1. T1 •*➡*[h, g] U2 →
-                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃h, L.ⓛV1⦄ ⊢ T1 •*➡*[h, g] T2 &
-                               U2 = ⓛ{a}V2. T2.
-#h #g #a #L #V1 #T1 #U2 * #X #H1 #H2
+lemma cpds_inv_abst1: ∀h,g,a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{a}V1.T1 •*➡*[h, g] U2 →
+                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 •*➡*[h, g] T2 &
+                               U2 = ⓛ{a}V2.T2.
+#h #g #a #G #L #V1 #T1 #U2 * #X #H1 #H2
 elim (sstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
 elim (cprs_inv_abst1 … H2) -H2 #V2 #T2 #HV12 #HUT2 #H destruct /3 width=5/
 qed-.
 
-lemma cpds_inv_abbr_abst: ∀h,g,a1,a2,L,V1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[h, g] ⓛ{a2}W2.T2 →
-                          ∃∃T. ⦃h, L.ⓓV1⦄ ⊢ T1 •*➡*[h, g] T & ⇧[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
-#h #g #a1 #a2 #L #V1 #W2 #T1 #T2 * #X #H1 #H2
+lemma cpds_inv_abbr_abst: ∀h,g,a1,a2,G,L,V1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[h, g] ⓛ{a2}W2.T2 →
+                          ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 •*➡*[h, g] T & ⇧[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
+#h #g #a1 #a2 #G #L #V1 #W2 #T1 #T2 * #X #H1 #H2
 elim (sstas_inv_bind1 … H1) -H1 #U1 #HTU1 #H destruct
 elim (cprs_inv_abbr1 … H2) -H2 *
 [ #V2 #U2 #HV12 #HU12 #H destruct
@@ -55,6 +55,6 @@ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma cpds_fwd_cpxs: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
-#h #g #L #T1 #T2 * /3 width=3 by cpxs_trans, sstas_cpxs, cprs_cpxs/
+lemma cpds_fwd_cpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
+#h #g #G #L #T1 #T2 * /3 width=3 by cpxs_trans, sstas_cpxs, cprs_cpxs/
 qed-.