milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / rdsx_csx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma
index 355ecb0047ee0ed834785d5d966e77b368d68bec..436c2b224e773585506878dce2200e3c5f85eb68 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma
@@ -21,16 +21,16 @@ include "basic_2/rt_computation/lsubsx_rdsx.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: lsx_lref_be_lpxs *)
-lemma rdsx_pair_lpxs (h) (o) (G):
-                     ∀K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
-                     ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
-                     ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
-#h #o #G #K1 #V #H
+lemma rdsx_pair_lpxs (h) (G):
+                     ∀K1,V. ⦃G, K1⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
+                     ∀K2. G ⊢ ⬈*[h, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
+                     ∀I. G ⊢ ⬈*[h, #0] 𝐒⦃K2.ⓑ{I}V⦄.
+#h #G #K1 #V #H
 @(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
 @(rdsx_ind … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
 @rdsx_intro #Y #HY #HnY
 elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
-elim (tdeq_dec h o V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
+elim (tdeq_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
 [ /5 width=5 by rdsx_rdeq_trans, lpxs_step_dx, rdeq_pair/
 | @(IHV0 … HnV02) -IHV0 -HnV02
   [ /2 width=3 by lpxs_cpx_trans/
@@ -41,10 +41,10 @@ elim (tdeq_dec h o V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
 qed.
 
 (* Basic_2A1: uses: lsx_lref_be *)
-lemma rdsx_lref_pair_drops (h) (o) (G):
-                           ∀K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
-                           ∀I,i,L. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
-#h #o #G #K #V #HV #HK #I #i elim i -i
+lemma rdsx_lref_pair_drops (h) (G):
+                           ∀K,V. ⦃G, K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → G ⊢ ⬈*[h, V] 𝐒⦃K⦄ →
+                           ∀I,i,L. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h, #i] 𝐒⦃L⦄.
+#h #G #K #V #HV #HK #I #i elim i -i
 [ #L #H >(drops_fwd_isid … H) -H /2 width=3 by rdsx_pair_lpxs/
 | #i #IH #L #H
   elim (drops_inv_bind2_isuni_next … H) -H // #J #Y #HY #H destruct
@@ -55,8 +55,8 @@ qed.
 (* Main properties **********************************************************)
 
 (* Basic_2A1: uses: csx_lsx *)
-theorem csx_rdsx (h) (o): ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
-#h #o #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
+theorem csx_rdsx (h): ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → G ⊢ ⬈*[h, T] 𝐒⦃L⦄.
+#h #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
 #Z #Y #X #IH #G #L * * //
 [ #i #HG #HL #HT #H destruct
   elim (csx_inv_lref … H) -H [ |*: * ]