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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "lambda-delta/substitution/drop_defs.ma".
17 (* DROPPING *****************************************************************)
19 (* the main properties ******************************************************)
21 axiom 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.
26 axiom drop_conf_lt: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
27 ∀e2,K2,I,V2. ↑[0, e2] K2. 𝕓{I} V2 ≡ L →
28 e2 < d1 → let d ≝ d1 - e2 - 1 in
29 ∃∃K1,V1. ↑[0, e2] K1. 𝕓{I} V1 ≡ L1 &
30 ↑[d, e1] K1 ≡ K2 & ↑[d,e1] V1 ≡ V2.
32 axiom drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
33 ∀e2,L2. ↑[0, e2] L2 ≡ L → e2 ≤ d1 →
34 ∃∃L0. ↑[0, e2] L0 ≡ L1 & ↑[d1 - e2, e1] L2 ≡ L0.
36 axiom drop_trans_ge: ∀d1,e1,L1,L. ↑[d1, e1] L ≡ L1 →
37 ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 ≤ e2 → ↑[0, e1 + e2] L2 ≡ L1.