⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → ⇩[i] L ≡ K.ⓑ{I}V → ∨∨
(∧∧ yinj i < d & I1 = I & V1 = V) |
(∧∧ (L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ → ⊥) & I1 = I & V1 = V) |
- (∧∧ d ≤ yinj i & L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ & I1 = I & V2 = V)
+ (∧∧ d ≤ yinj i & L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ & I2 = I & V2 = V)
).
interpretation
(* Basic properties *********************************************************)
+(* Note: this can be proved by llor_skip *)
lemma llor_atom: ∀L2,T,d. ⋆ ⩖[T, d] L2 ≡ ⋆.
#L2 #T #d @and3_intro //
#I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
lemma llor_skip: ∀L1,L2,U,d. |L1| ≤ |L2| → yinj (|L1|) ≤ d → L1 ⩖[U, d] L2 ≡ L1.
#L1 #L2 #U #d #HL12 #Hd @and3_intro // -HL12
-#I1 #I2 #I #K1 #K2 #K #W1 #W2 #W #i #HLK1 #_ #HLK -I2 -L2 -K2
+#I1 #I2 #I #K1 #K2 #K #W1 #W2 #W #i #HLK1 #_ #HLK -L2 -K2
lapply (ldrop_mono … HLK … HLK1) -HLK #H destruct
lapply (ldrop_fwd_length_lt2 … HLK1) -K1
/5 width=3 by ylt_yle_trans, ylt_inj, or3_intro0, and3_intro/