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Proof step 8 from proof i2np (previous step)

0 ≤ j, 0 ≤ i0, ∀ 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 + j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intnat inst: name: add seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i) + i→n(j) = i→n(i + j) subst: [j, i] → [j, i0 * j] flags: rewrite, current

Additional information

Used simplifier rules: zero-ge-02: ⊦ 0 ≤ i → (0 ≤ i * j ↔ ¬ ¬(i = 0 ∨ 0 ≤ j)); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j, i0 * j