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Proof step 24 from proof completeness (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
x2 = x, x ≠ [], max(x) < 0, head(x) ≤ max(x), head(x) < 0 ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 = fail → (∀ t. x2 ≠ depths(t, 0)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ head(x) ∈ x ↔ x ≠ []])]]