1. 1
2. 2
3. 3
4. 4
5. 5
6. 6
7. 7
8. 8
9. 9
10. 10
11. 11
12. 12
13. 13
14. 14
15. 15
16. 16
17. 17
18. 18
19. 19
20. 20
21. 21
22. 22
23. 23
24. 24
25. 25
26. 26
27. 27
28. 28
29. 29
30. 30
31. 31
32. 32
33. 33
34. 34
35. 35
36. 36
37. 37
38. 38
39. 39
40. 40

import Std.Tactic.Do

def change_between (xs : Array Nat) (i s : Nat) : Array Nat := Id.run do
  let mut xs := xs
  for k in List.range' i s do
    xs := xs.modify k (· * 3)
  return xs

def equiv_change_between (xs : Array Nat) (i s : Nat) : Array Nat :=
  Array.ofFn fun (k : Fin xs.size) =>
    if ↑k ∈ List.range' i s then
      xs[k] * 3
    else
      xs[k]

#eval equiv_change_between #[1, 2, 3, 4, 5, 6] 2 3
#eval change_between #[1, 2, 3, 4, 5, 6] 2 3

open Std.Do in
def change_between_spec (xs : Array Nat) (i s : Nat) :
  change_between xs i s = equiv_change_between xs i s := by
  simp [equiv_change_between]
  generalize h : change_between xs i s = x
  apply Id.of_wp_run_eq h
  mvcgen invariants
  · ⇓⟨c, xs'⟩ => ⌜xs.size = xs'.size ∧ xs' = (Array.ofFn fun (k : Fin xs.size) =>
    if k < i + c.prefix.length ∧ ↑k ∈ List.range' i s then
      xs[k] * 3
    else
      xs[k])⌝
  all_goals expose_names
  · constructor
    · grind
    · simp [h_2.2]
      ext <;> simp [Array.getElem_modify]
      grind
  · simp
    ext <;> simp
    grind
  · grind