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Proof step 51 from proof harness-2 (previous step)

x = 3 ' + 2 ' + 2 ', to4 = fail, x1 = x ∧ d0 = 1 ⊦ 〈if is_empty(x1) then to := fail else let h = head(x1) in if h < d0 then to := fail else if h = d0 then { x1 := pop(x1) ; to := some(Leaf) } else let to0 = fail, to1 = fail in { build_rec#(d0 + 1; x1, to0) ; if to0 = fail then to := fail else { build_rec#(d0 + 1; x1, to1) ; if to1 = fail then to := fail else to := some(Node(to0 .t, to1 .t)) } }〉〈to4 := to ; if to4 = fail then to0 := fail else to0 := some(Node(Leaf, to4 .t))〉〈to1 := to0 ; if x1 ≠ [] then to1 := fail〉 to1 = fail

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 50:
x = 3 ' + 2 ' + 2 ', to4 = fail, x1 = x ∧ d0 = 1 ⊦ 〈let h = head(x1) in if h < d0 then to := fail else if h = d0 then { x1 := pop(x1) ; to := some(Leaf) } else let to0 = fail, to1 = fail in { build_rec#(d0 + 1; x1, to0) ; if to0 = fail then to := fail else { build_rec#(d0 + 1; x1, to1) ; if to1 = fail then to := fail else to := some(Node(to0 .t, to1 .t)) } }〉〈to4 := to ; if to4 = fail then to0 := fail else to0 := some(Node(Leaf, to4 .t))〉〈to1 := to0 ; if x1 ≠ [] then to1 := fail〉 to1 = fail

Rule argument

[fmapos-arg: pos: right 1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_empty(x) ↔ x = []], [CSIMPSEQ : ⊦ d ' + x ≠ []], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z])]]