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 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
  25 [ //
  26 | #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2
  27   lapply (drop_inv_drop1 … H ?) -H /2/ #HL2
  28   <minus_plus_comm /3/
  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/ ]
  34 ]
  35 qed.
  36
  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.
  42
  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.
  46
  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.