matita/matita/contribs/lambdadelta/basic_2/substitution/gr2_plus.ma

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  14
  15 include "basic_2/substitution/gr2.ma".
  16
  17 (* GENERIC RELOCATION WITH PAIRS ********************************************)
  18
  19 let rec pluss (des:list2 nat nat) (i:nat) on des ≝ match des with
  20 [ nil2          ⇒ ⟠
  21 | cons2 d e des ⇒ {d + i, e} @ pluss des i
  22 ].
  23
  24 interpretation "plus (generic relocation with pairs)"
  25    'plus x y = (pluss x y).
  26
  27 (* Basic inversion lemmas ***************************************************)
  28
  29 lemma pluss_inv_nil2: ∀i,des. des + i = ⟠ → des = ⟠.
  30 #i * // normalize
  31 #d #e #des #H destruct
  32 qed.
  33
  34 lemma pluss_inv_cons2: ∀i,d,e,des2,des. des + i = {d, e} @ des2 →
  35                        ∃∃des1. des1 + i = des2 & des = {d - i, e} @ des1.
  36 #i #d #e #des2 * normalize
  37 [ #H destruct
  38 | #d1 #e1 #des1 #H destruct /2 width=3/
  39 ]
  40 qed-.