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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "lambda-delta/substitution/drop_defs.ma".
17 (* DROPPING *****************************************************************)
19 (* the main properties ******************************************************)
21 lemma drop_conf_ge: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
22 ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 + e1 ≤ e2 →
23 ↑[0, e2 - e1] L2 ≡ L1.
24 #d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
26 | #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2
27 lapply (drop_inv_drop1 … H ?) -H /2/ #HL2
29 | #L #K #I #V1 #V2 #d #e #_ #_ #IHLK #e2 #L2 #H #Hdee2
30 lapply (transitive_le 1 … Hdee2) // #He2
31 lapply (drop_inv_drop1 … H ?) -H // -He2 #HL2
32 lapply (transitive_le (1+e) … Hdee2) // #Hee2
33 >(plus_minus_m_m (e2-e) 1 ?) [ @drop_drop >minus_minus_comm /3/ | /2/ ]
37 axiom drop_conf_lt: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
38 ∀e2,K2,I,V2. ↑[0, e2] K2. 𝕓{I} V2 ≡ L →
39 e2 < d1 → let d ≝ d1 - e2 - 1 in
40 ∃∃K1,V1. ↑[0, e2] K1. 𝕓{I} V1 ≡ L1 &
41 ↑[d, e1] K1 ≡ K2 & ↑[d,e1] V1 ≡ V2.
43 axiom drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
44 ∀e2,L2. ↑[0, e2] L2 ≡ L → e2 ≤ d1 →
45 ∃∃L0. ↑[0, e2] L0 ≡ L1 & ↑[d1 - e2, e1] L2 ≡ L0.
47 axiom drop_trans_ge: ∀d1,e1,L1,L. ↑[d1, e1] L ≡ L1 →
48 ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 ≤ e2 → ↑[0, e1 + e2] L2 ≡ L1.