(* Alternative definition ***************************************************)
-lemma llor_tail_frees: ∀L1,L2,L,U,d. L1 ⋓[U, d] L2 ≡ L → d ≤ yinj (|L1|) →
- ∀I1,W1. ⓑ{I1}W1.L1 ⊢ |L1| ϵ 𝐅*[d]⦃U⦄ →
- ∀I2,W2. ⓑ{I1}W1.L1 ⋓[U, d] ⓑ{I2}W2.L2 ≡ ⓑ{I2}W2.L.
-#L1 #L2 #L #U #d * #HL12 #HL1 #IH #Hd #I1 #W1 #HU #I2 #W2
+lemma llor_tail_frees: ∀L1,L2,L,U,l. L1 ⋓[U, l] L2 ≡ L → l ≤ yinj (|L1|) →
+ ∀I1,W1. ⓑ{I1}W1.L1 ⊢ |L1| ϵ 𝐅*[l]⦃U⦄ →
+ ∀I2,W2. ⓑ{I1}W1.L1 ⋓[U, l] ⓑ{I2}W2.L2 ≡ ⓑ{I2}W2.L.
+#L1 #L2 #L #U #l * #HL12 #HL1 #IH #Hl #I1 #W1 #HU #I2 #W2
@and3_intro [1,2: >ltail_length /2 width=1 by le_S_S/ ]
#J1 #J2 #J #K1 #K2 #K #V1 #V2 #V #i #HLK1 #HLK2 #HLK
lapply (drop_fwd_length_lt2 … HLK1) >ltail_length #H
]
qed.
-lemma llor_tail_cofrees: ∀L1,L2,L,U,d. L1 ⋓[U, d] L2 ≡ L →
- ∀I1,W1. (ⓑ{I1}W1.L1 ⊢ |L1| ϵ 𝐅*[d]⦃U⦄ → ⊥) →
- ∀I2,W2. ⓑ{I1}W1.L1 ⋓[U, d] ⓑ{I2}W2.L2 ≡ ⓑ{I1}W1.L.
-#L1 #L2 #L #U #d * #HL12 #HL1 #IH #I1 #W1 #HU #I2 #W2
+lemma llor_tail_cofrees: ∀L1,L2,L,U,l. L1 ⋓[U, l] L2 ≡ L →
+ ∀I1,W1. (ⓑ{I1}W1.L1 ⊢ |L1| ϵ 𝐅*[l]⦃U⦄ → ⊥) →
+ ∀I2,W2. ⓑ{I1}W1.L1 ⋓[U, l] ⓑ{I2}W2.L2 ≡ ⓑ{I1}W1.L.
+#L1 #L2 #L #U #l * #HL12 #HL1 #IH #I1 #W1 #HU #I2 #W2
@and3_intro [1,2: >ltail_length /2 width=1 by le_S_S/ ]
#J1 #J2 #J #K1 #K2 #K #V1 #V2 #V #i #HLK1 #HLK2 #HLK
lapply (drop_fwd_length_lt2 … HLK1) >ltail_length #H