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Proof step 7 from proof i2n-mod (previous step)

j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i0 ⊦ i→n(j0) = (i→n(i0 * j) + i→n(j0)) % i→n(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j)
Proof step 9:
0 ≤ i0 ∧ 0 ≤ j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i0 ⊦ i→n(j0) = (i→n(i0) * i→n(j) + i→n(j0)) % i→n(j)

Rule argument

spec: intnat inst: name: i2n-mult seq: ⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j) subst: [j, i] → [j, i0] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, i0