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

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  14
  15 include "lambda-delta/substitution/drop_defs.ma".
  16
  17 (* DROPPING *****************************************************************)
  18
  19 (* the main properties ******************************************************)
  20
  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.
  24
  25 axiom drop_conf_lt: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
  26                     ∀e2,K2,I,V2. ↑[0, e2] K2. 𝕓{I} V2 ≡ L →
  27                     e2 < d1 → let d ≝ d1 - e2 - 1 in
  28                     ∃∃K1,V1. ↑[0, e2] K1. 𝕓{I} V1 ≡ L1 &
  29                              ↑[d, e1] K2 ≡ K1 & ↑[d,e1] V1 ≡ V2.
  30
  31 axiom drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
  32                      ∀e2,L2. ↑[0, e2] L2 ≡ L → e2 ≤ d1 →
  33                      ∃∃L0. ↑[0, e2] L0 ≡ L1 & ↑[d1 - e2, e1] L2 ≡ L0.
  34
  35 axiom drop_trans_ge: ∀d1,e1,L1,L. ↑[d1, e1] L ≡ L1 →
  36                      ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 ≤ e2 → ↑[0, e1 + e2] L2 ≡ L1.