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Proof step 22 from proof soundness (previous step)

x = d ' + y, d < 0, max(d ' + y) < 0, d ≤ max(d ' + y) ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 ≠ fail → d ' + y = depths(to0 .t, 0))

Heuristic weak unfold applied rule call right

And obtained the following new goals

Proof step 13:
⊦
Proof step 21:
x = d ' + y, d < 0, max(d ' + y) < 0, d ≤ max(d ' + y) ⊦ 〈x0 := x, d0 := 0〉〈if is_empty(x0) then to0 := fail else let h = head(x0) in if h < d0 then to0 := fail else if h = d0 then { x0 := pop(x0) ; to0 := some(Leaf) } else let to2 = fail, to1 = fail in { build_rec#(d0 + 1; x0, to2) ; if to2 = fail then to0 := fail else { build_rec#(d0 + 1; x0, to1) ; if to1 = fail then to0 := fail else to0 := some(Node(to2 .t, to1 .t)) } }〉〈to1 := to0, x1 := x0 ; if x1 ≠ [] then to1 := fail〉 (to1 ≠ fail → d ' + y = depths(to1 .t, 0))

Rule argument

[fmapos-arg: pos: right 1]

Additional information

[[CONCRETESIMPRULES : ()]]