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Proof step 42 from proof completeness (previous step)

〈build_rec#(0; x, to)〉 (x = x1 ∧ to = to1), x2 = x, x ≠ [], 0 ≤ max(x), x0 = x, to1 ≠ fail → x0 = depths(to1 .t, 0) + x1, to2 = to1 ∧ x3 = x1 ⊦ 〈if x3 ≠ [] then to2 := fail〉 (to2 = fail → (∀ t. x2 ≠ depths(t, 0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
〈build_rec#(0; x, to)〉 (x = x1 ∧ to = to1), x ≠ [], 0 ≤ max(x), to1 ≠ fail → x = depths(to1 .t, 0) + x1 ⊦ 〈if x1 ≠ [] then to1 := fail〉 (to1 = fail → (∀ t. x ≠ depths(t, 0)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]