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Proof step 11 from proof soundness (previous step)

x2 = x, x = [] ∨ ¬ 0 ≤ max(x), x = [] ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 ≠ fail → x2 = depths(to0 .t, 0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
x = [] ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 to0 = fail

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ depths(t, i) ≠ []])]]