- some renaming according to the written version of basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs.ma
index 588208177e01d4b1ecb664f933aed770a523e4cc..75c56d8a43d7fa67ad31e181cf76aacc37158337 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs.ma
@@ -64,13 +64,13 @@ lemma cprs_cpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢
 #h #g #G #L #T1 #T2 #H @(cprs_ind … H) -T2 /3 width=3 by cpxs_strap1, cpr_cpx/
 qed.
 
-lemma cpxs_sort: ∀h,g,G,L,k,l1. deg h g k l1 →
-                 ∀l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ ⋆k ➡*[h, g] ⋆((next h)^l2 k).
-#h #g #G #L #k #l1 #Hkl1 #l2 @(nat_ind_plus … l2) -l2 /2 width=1 by cpx_cpxs/
-#l2 #IHl2 #Hl21 >iter_SO
-@(cpxs_strap1 … (⋆(iter l2 ℕ (next h) k)))
+lemma cpxs_sort: ∀h,g,G,L,k,d1. deg h g k d1 →
+                 ∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ ⋆k ➡*[h, g] ⋆((next h)^d2 k).
+#h #g #G #L #k #d1 #Hkd1 #d2 @(nat_ind_plus … d2) -d2 /2 width=1 by cpx_cpxs/
+#d2 #IHd2 #Hd21 >iter_SO
+@(cpxs_strap1 … (⋆(iter d2 ℕ (next h) k)))
 [ /3 width=3 by lt_to_le/
-| @(cpx_st … (l1-l2-1)) <plus_minus_m_m
+| @(cpx_st … (d1-d2-1)) <plus_minus_m_m
   /2 width=1 by deg_iter, monotonic_le_minus_r/
 ]
 qed.
@@ -102,7 +102,7 @@ lemma cpxs_pair_sn: ∀h,g,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 →
 /3 width=3 by cpxs_strap1, cpx_pair_sn/
 qed.
 
-lemma cpxs_zeta: â\88\80h,g,G,L,V,T1,T,T2. â\87§[0, 1] T2 ≡ T →
+lemma cpxs_zeta: â\88\80h,g,G,L,V,T1,T,T2. â¬\86[0, 1] T2 ≡ T →
                  ⦃G, L.ⓓV⦄ ⊢ T1 ➡*[h, g] T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡*[h, g] T2.
 #h #g #G #L #V #T1 #T #T2 #HT2 #H @(cpxs_ind_dx … H) -T1
 /3 width=3 by cpxs_strap2, cpx_cpxs, cpx_bind, cpx_zeta/
@@ -128,7 +128,7 @@ lemma cpxs_beta_dx: ∀h,g,a,G,L,V1,V2,W1,W2,T1,T2.
 qed.
 
 lemma cpxs_theta_dx: ∀h,g,a,G,L,V1,V,V2,W1,W2,T1,T2.
-                     â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V â\86\92 â\87§[0, 1] V ≡ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 →
+                     â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V â\86\92 â¬\86[0, 1] V ≡ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 →
                      ⦃G, L⦄ ⊢ W1 ➡[h, g] W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h, g] ⓓ{a}W2.ⓐV2.T2.
 #h #g #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2 
 /4 width=9 by cpx_cpxs, cpxs_strap1, cpxs_bind_dx, cpxs_flat_dx, cpx_theta/
@@ -137,15 +137,15 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 lemma cpxs_inv_sort1: ∀h,g,G,L,U2,k. ⦃G, L⦄ ⊢ ⋆k ➡*[h, g] U2 →
-                      ∃∃n,l. deg h g k (n+l) & U2 = ⋆((next h)^n k).
+                      ∃∃n,d. deg h g k (n+d) & U2 = ⋆((next h)^n k).
 #h #g #G #L #U2 #k #H @(cpxs_ind … H) -U2
-[ elim (deg_total h g k) #l #Hkl
-  @(ex2_2_intro … 0 … Hkl) -Hkl //
-| #U #U2 #_ #HU2 * #n #l #Hknl #H destruct
+[ elim (deg_total h g k) #d #Hkd
+  @(ex2_2_intro … 0 … Hkd) -Hkd //
+| #U #U2 #_ #HU2 * #n #d #Hknd #H destruct
   elim (cpx_inv_sort1 … HU2) -HU2
   [ #H destruct /2 width=4 by ex2_2_intro/
-  | * #l0 #Hkl0 #H destruct -l
-    @(ex2_2_intro … (n+1) l0) /2 width=1 by deg_inv_prec/ >iter_SO //
+  | * #d0 #Hkd0 #H destruct -d
+    @(ex2_2_intro … (n+1) d0) /2 width=1 by deg_inv_prec/ >iter_SO //
   ]
 ]
 qed-.