[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 20 from proof completeness (previous step)

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 → (∀ t. d ' + y ≠ depths(t, 0)))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 19:
x = d ' + y, d < 0, max(d ' + y) < 0, d ≤ max(d ' + y), x2 = x ∧ d1 = 0 ⊦ 〈if is_empty(x2) then to0 := fail else let h = head(x2) in if h < d1 then to0 := fail else if h = d1 then { x2 := pop(x2) ; to0 := some(Leaf) } else let to2 = fail, to1 = fail in { build_rec#(d1 + 1; x2, to2) ; if to2 = fail then to0 := fail else { build_rec#(d1 + 1; x2, to1) ; if to1 = fail then to0 := fail else to0 := some(Node(to2 .t, to1 .t)) } }〉〈to1 := to0, x1 := x2 ; if x1 ≠ [] then to1 := fail〉 (to1 = fail → (∀ t. d ' + y ≠ depths(t, 0)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]