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Proof step 11 from proof i2np (previous step)

0 ≤ i0, 0 ≤ i0 * j, 0 ≤ j, ∀ j0. 0 ≤ j0 → i→n(i0) * i→n(j0) = i→n(i0 * j0) ⊦ i→n(j) * i→n(i0) + i→n(j) = i→n(i0 * j) + i→n(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 ≤ i → (0 ≤ i * j ↔ i = 0 ∨ 0 ≤ j); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)