minor update

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / lleq_alt_rec.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_alt_rec.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_alt_rec.ma
index 692ece149c1a928433a324e411dacf00c78903ad..440e0f510678d3374ebc7da9b80257b00cb4e435 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_alt_rec.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/lleq_alt_rec.ma
@@ -19,36 +19,36 @@ include "basic_2/multiple/lleq.ma".
 
 (* Alternative definition (recursive) ***************************************)
 
-theorem lleq_intro_alt_r: ∀L1,L2,T,d. |L1| = |L2| →
-                          (∀I1,I2,K1,K2,V1,V2,i. d ≤ yinj i → (∀U. ⬆[i, 1] U ≡ T → ⊥) →
+theorem lleq_intro_alt_r: ∀L1,L2,T,l. |L1| = |L2| →
+                          (∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → (∀U. ⬆[i, 1] U ≡ T → ⊥) →
                              ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
                              ∧∧ I1 = I2 & V1 = V2 & K1 ≡[V1, 0] K2
-                          ) → L1 ≡[T, d] L2.
-#L1 #L2 #T #d #HL12 #IH @llpx_sn_intro_alt_r // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hid #HnT #HLK1 #HLK2
+                          ) → L1 ≡[T, l] L2.
+#L1 #L2 #T #l #HL12 #IH @llpx_sn_intro_alt_r // -HL12
+#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
 elim (IH … HnT HLK1 HLK2) -IH -HnT -HLK1 -HLK2 /2 width=1 by and3_intro/
 qed.
 
 theorem lleq_ind_alt_r: ∀S:relation4 ynat term lenv lenv.
-                        (∀L1,L2,T,d. |L1| = |L2| → (
-                           ∀I1,I2,K1,K2,V1,V2,i. d ≤ yinj i → (∀U. ⬆[i, 1] U ≡ T → ⊥) →
+                        (∀L1,L2,T,l. |L1| = |L2| → (
+                           ∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → (∀U. ⬆[i, 1] U ≡ T → ⊥) →
                            ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
                            ∧∧ I1 = I2 & V1 = V2 & K1 ≡[V1, 0] K2 & S 0 V1 K1 K2
-                        ) → S d T L1 L2) →
-                        ∀L1,L2,T,d. L1 ≡[T, d] L2 → S d T L1 L2.
-#S #IH1 #L1 #L2 #T #d #H @(llpx_sn_ind_alt_r … H) -L1 -L2 -T -d
-#L1 #L2 #T #d #HL12 #IH2 @IH1 -IH1 // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hid #HnT #HLK1 #HLK2
+                        ) → S l T L1 L2) →
+                        ∀L1,L2,T,l. L1 ≡[T, l] L2 → S l T L1 L2.
+#S #IH1 #L1 #L2 #T #l #H @(llpx_sn_ind_alt_r … H) -L1 -L2 -T -l
+#L1 #L2 #T #l #HL12 #IH2 @IH1 -IH1 // -HL12
+#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
 elim (IH2 … HnT HLK1 HLK2) -IH2 -HnT -HLK1 -HLK2 /2 width=1 by and4_intro/
 qed-.
 
-theorem lleq_inv_alt_r: ∀L1,L2,T,d. L1 ≡[T, d] L2 →
+theorem lleq_inv_alt_r: ∀L1,L2,T,l. L1 ≡[T, l] L2 →
                         |L1| = |L2| ∧
-                        ∀I1,I2,K1,K2,V1,V2,i. d ≤ yinj i → (∀U. ⬆[i, 1] U ≡ T → ⊥) →
+                        ∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → (∀U. ⬆[i, 1] U ≡ T → ⊥) →
                         ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
                         ∧∧ I1 = I2 & V1 = V2 & K1 ≡[V1, 0] K2.
-#L1 #L2 #T #d #H elim (llpx_sn_inv_alt_r … H) -H
+#L1 #L2 #T #l #H elim (llpx_sn_inv_alt_r … H) -H
 #HL12 #IH @conj //
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hid #HnT #HLK1 #HLK2
+#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
 elim (IH … HnT HLK1 HLK2) -IH -HnT -HLK1 -HLK2 /2 width=1 by and3_intro/
 qed-.