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Proof step 13 from proof i2np (previous step)

0 ≤ i0 -1, 0 ≤ j, ∀ j. 0 ≤ j ∧ 0 ≤ i0 → i→n(i0) * i→n(j) = i→n(i0 * j) ⊦ i→n(i0 -1) * i→n(j) = i→n(i0 -1 * j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 < i0, 0 ≤ j, ∀ j. 0 ≤ j ∧ 0 ≤ i0 → i→n(i0) * i→n(j) = i→n(i0 * j) ⊦ (i→n(i0) - 1) * i→n(j) = i→n((i0 - 1) * j)

Rule argument

Additional information

Used simplifier rules: sub: j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j);%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i ≤ j → ¬ j < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i -1 = i - 1; (s)