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Proof step 27 from proof completeness (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
x2 = x, x = [] ∨ ¬ 0 ≤ max(x), x = [] ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 = fail → (∀ t. x2 ≠ depths(t, 0)))
Proof step 26:
x2 = x, x = [] ∨ ¬ 0 ≤ max(x), x ≠ [] ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 = fail → (∀ t. x2 ≠ depths(t, 0)))

Rule argument

[fma-arg: x = []]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (x = [])]]