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Proof step 19 from proof i2np (previous step)

i→n(j) * i→n(i1) + i→n(j) = i→n(i1 * j + 1 * j), 0 ≤ j, 0 ≤ i1, ∀ j0. 0 ≤ j0 → i→n(j0) * i→n(i1) + i→n(j0) = i→n((i1 + 1) * j0) ⊦ i→n(i1) * i→n(j) = i→n(i1 * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: add-01 seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j) subst: [j, i] → [1 * j, i1 * j] flags: rewrite, current

Additional information

Used simplifier rules: one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%mult-c: ⊦ m * n = n * m; from specification nat-mult%zero-ge-02: ⊦ 0 ≤ i → (0 ≤ i * j ↔ ¬ ¬(i = 0 ∨ 0 ≤ j)); from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: 1 * j, i1 * j