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14
15 include "ground/notation/functions/upspoonstar_2.ma".
16 include "ground/arith/nat_succ_iter.ma".
17 include "ground/relocation/pr_map.ma".
18
19 (* ITERATED PUSH FOR PARTIAL RELOCATION MAPS ********************************)
20
21 (*** pushs *)
22 definition pr_pushs (f:pr_map) (n:nat) ≝
23            (pr_push^n) f.
24
25 interpretation
26   "iterated push (partial relocation maps)"
27   'UpSpoonStar n f = (pr_pushs f n).
28
29 (* Basic constructions ******************************************************)
30
31 (*** pushs_O *)
32 lemma pr_pushs_zero:
33       ∀f. f = ⫯*[𝟎] f.
34 // qed.
35
36 (*** push_swap *)
37 lemma pr_pushs_push (n):
38       ∀f. ⫯⫯*[n] f = ⫯*[n] ⫯f.
39 #n #f @(niter_appl … pr_push)
40 qed.
41
42 (*** pushs_S *)
43 lemma pr_pushs_succ (n):
44       ∀f. ⫯⫯*[n] f = ⫯*[↑n] f.
45 #f #n @(niter_succ … pr_push)
46 qed.
47
48 (*** pushs_xn *)
49 lemma pr_pushs_swap (n):
50       ∀f. ⫯*[n] ⫯f = ⫯*[↑n] f.
51 // qed.