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Proof step 9 from proof countrefs2-pos (previous step)

i ≤ 0, countrefs2(i ' + ints0) < 0, 0 ≤ countrefs2(ints0) ⊦ ints0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ # ints > 1 ∧ ints .first > 0 → countrefs2(ints) = ints .first + ints .first * countrefs2(ints .rest)
Proof step 8:
¬ (# (i ' + ints0) > 1 ∧ (i ' + ints0) .first > 0), i ≤ 0, countrefs2(i ' + ints0) < 0, 0 ≤ countrefs2(ints0) ⊦ ints0 = []

Rule argument

[crewrite-arg: countrefs_more_gr0, F, [ints] → [i ' + ints0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ m > n ↔ n < m], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i ' + ints0)]]