lemma lt_plus_SO_to_le: ∀x,y. x < y + 1 → x ≤ y.
/2 width=1 by monotonic_pred/ qed-.
-(*
+
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 ≡ ⓑ{I1}W2.L.
+ ∀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
@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
| #HnU #HZ #HX
| #Hdi #H2U #HZ #HX
]
-| -IH destruct
- lapply (ldrop_O1_inv_append1_le … HLK1 … (⋆) ?) // -HLK1 normalize #H destruct
- lapply (ldrop_O1_inv_append1_le … HLK2 … HL12)
+| -IH -HLK1 destruct
+ lapply (ldrop_O1_inv_append1_le … HLK2 … (⋆) ?) // -HLK2 normalize #H destruct
lapply (ldrop_O1_inv_append1_le … HLK … (⋆) ?) // -HLK normalize #H destruct
- @or3_intro2 @and4_intro /2 width=1 by ylt_fwd_le/
+ /4 width=1 by ylt_fwd_le, or3_intro2, and4_intro/
]
-*)