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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 "ground_2/relocation/mr2.ma".
17 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
19 rec definition pluss (cs:mr2) (i:nat) on cs ≝ match cs with
21 | cons2 l m cs ⇒ {l + i,m};pluss cs i
24 interpretation "plus (multiple relocation with pairs)"
25 'plus x y = (pluss x y).
27 (* Basic properties *********************************************************)
29 lemma pluss_SO2: ∀l,m,cs. ({l,m};cs) + 1 = {↑l,m};cs + 1.
32 (* Basic inversion lemmas ***************************************************)
34 lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
39 lemma pluss_inv_cons2: ∀i,l,m,cs2,cs. cs + i = {l,m};cs2 →
40 ∃∃cs1. cs1 + i = cs2 & cs = {l - i,m};cs1.
42 [ normalize #H destruct
43 | #l1 #m1 #cs1 whd in ⊢ (??%?→?); #H destruct
44 <minus_plus_m_m /2 width=3 by ex2_intro/