(* Main properties **********************************************************)
-(* Basic_1: was: ldrop_mono *)
+(* Basic_1: was: drop_mono *)
theorem ldrop_mono: ∀d,e,L,L1. ⇩[d, e] L ≡ L1 →
∀L2. ⇩[d, e] L ≡ L2 → L1 = L2.
#d #e #L #L1 #H elim H -d -e -L -L1
]
qed-.
-(* Basic_1: was: ldrop_conf_ge *)
+(* Basic_1: was: drop_conf_ge *)
theorem ldrop_conf_ge: ∀d1,e1,L,L1. ⇩[d1, e1] L ≡ L1 →
∀e2,L2. ⇩[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
⇩[0, e2 - e1] L1 ≡ L2.
]
qed.
-(* Basic_1: was: ldrop_conf_lt *)
+(* Basic_1: was: drop_conf_lt *)
theorem ldrop_conf_lt: ∀d1,e1,L,L1. ⇩[d1, e1] L ≡ L1 →
- ∀e2,K2,I,V2. ⇩[0, e2] L ≡ K2. 𝕓{I} V2 →
+ ∀e2,K2,I,V2. ⇩[0, e2] L ≡ K2. ⓑ{I} V2 →
e2 < d1 → let d ≝ d1 - e2 - 1 in
- ∃∃K1,V1. ⇩[0, e2] L1 ≡ K1. 𝕓{I} V1 &
+ ∃∃K1,V1. ⇩[0, e2] L1 ≡ K1. ⓑ{I} V1 &
⇩[d, e1] K2 ≡ K1 & ⇧[d, e1] V1 ≡ V2.
#d1 #e1 #L #L1 #H elim H -d1 -e1 -L -L1
[ #d #e #e2 #K2 #I #V2 #H
]
qed.
-(* Basic_1: was: ldrop_trans_le *)
+(* Basic_1: was: drop_trans_le *)
theorem ldrop_trans_le: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L →
∀e2,L2. ⇩[0, e2] L ≡ L2 → e2 ≤ d1 →
∃∃L0. ⇩[0, e2] L1 ≡ L0 & ⇩[d1 - e2, e1] L0 ≡ L2.
]
qed.
-(* Basic_1: was: ldrop_trans_ge *)
+(* Basic_1: was: drop_trans_ge *)
theorem ldrop_trans_ge: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L →
∀e2,L2. ⇩[0, e2] L ≡ L2 → d1 ≤ e2 → ⇩[0, e1 + e2] L1 ≡ L2.
#d1 #e1 #L1 #L #H elim H -d1 -e1 -L1 -L
#e1 #e1 #e2 >commutative_plus /2 width=5/
qed.
-(* Basic_1: was: ldrop_conf_rev *)
+(* Basic_1: was: drop_conf_rev *)
axiom ldrop_div: ∀e1,L1,L. ⇩[0, e1] L1 ≡ L → ∀e2,L2. ⇩[0, e2] L2 ≡ L →
∃∃L0. ⇩[0, e1] L0 ≡ L2 & ⇩[e1, e2] L0 ≡ L1.