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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "lambda-delta/substitution/thin_defs.ma".
17 (* THINNING *****************************************************************)
19 (* the main properties ******************************************************)
21 axiom thin_conf_ge: ∀d1,e1,L,L1. ↓[d1,e1] L ≡ L1 →
22 ∀e2,L2. ↓[0,e2] L ≡ L2 → d1 + e1 ≤ e2 → ↓[0,e2-e1] L1 ≡ L2.
24 axiom thin_conf_lt: ∀d1,e1,L,L1. ↓[d1,e1] L ≡ L1 →
25 ∀e2,K2,I,V2. ↓[0,e2] L ≡ K2. 𝕓{I} V2 →
26 e2 < d1 → let d ≝ d1 - e2 - 1 in
27 ∃∃K1,V1. ↓[0,e2] L1 ≡ K1. 𝕓{I} V1 & ↓[d,e1] K2 ≡ K1 & ↑[d,e1] V1 ≡ V2.
29 axiom thin_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
30 ∀e2,L2. ↓[0, e2] L ≡ L2 → e2 ≤ d1 →
31 ∃∃L0. ↓[0, e2] L1 ≡ L0 & ↓[d1 - e2, e1] L0 ≡ L2.
33 axiom thin_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
34 ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 ≤ e2 → ↓[0, e1 + e2] L1 ≡ L2.