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15 include "ground_2/ynat/ynat_plus.ma".
16 include "basic_2/multiple/mr2.ma".
18 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
20 let rec pluss (cs:list2 ynat nat) (i:nat) on cs ≝ match cs with
22 | cons2 l m cs ⇒ {l + i, m} @ pluss cs i
25 interpretation "plus (multiple relocation with pairs)"
26 'plus x y = (pluss x y).
28 (* Basic properties *********************************************************)
30 lemma pluss_SO2: ∀l,m,cs. ({l, m} @ cs) + 1 = {⫯l, m} @ cs + 1.
33 (* Basic inversion lemmas ***************************************************)
35 lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
40 lemma pluss_inv_cons2: ∀i,l,m,cs2,cs. cs + i = {l, m} @ cs2 →
41 ∃∃cs1. cs1 + i = cs2 & cs = {l - i, m} @ cs1.
43 [ normalize #H destruct
44 | #l1 #m1 #cs1 whd in ⊢ (??%?→?); #H destruct
45 >yplus_minus_inj /2 width=3 by ex2_intro/