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Proof step 8 from proof countrefs-i2n (previous step)

0 ≤ i2, 0 ≤ (i2 + 1) * countrefs(ints) ⊦ i→n((i2 + 1) * countrefs(ints)) = i→n(countrefs(ints)) * i→n(i2) + i→n(countrefs(ints))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j)
Proof step 7:
⊦ ¬ countrefs(ints) < 0

Rule argument

[speclemmaarg: ,0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j) ,[j, i] → [countrefs(ints), i2 + 1] ,F ,intnat , ,i2n-mult ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m * (n + 1) = m * n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0])], [EXTRATERMS : (countrefs(ints), i2 + 1)]]