matita/matita/lib/lambda-delta/substitution/thin_main.ma

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  14
  15 include "lambda-delta/substitution/thin_defs.ma".
  16
  17 (* THINNING *****************************************************************)
  18
  19 (* the main properties ******************************************************)
  20
  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.
  23
  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.
  28
  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.
  32
  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.