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Proof step 30 from proof noeth-modlep (previous step)

i1 < j2, 0 < j2, j0 < j2, i0 < i, j0 ≤ i1, 0 ≤ i1, 0 ≤ j0, i1 * i + i ≤ (i1 + 1) * i0 + j0 ⊦ j0 < i1 ∧ i1 * i ≤ i1 * i0 + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 32:
i0 < i, j0 < j2, 0 < j2, i1 < j2, i1 * i + i ≤ (i1 * i0 + 1 * i0) + j0, 0 ≤ j0, 0 ≤ i1, j0 ≤ i1 ⊦ j0 < i1 ∧ i1 * i ≤ i1 * i0 + j0

Rule argument

spec: <toplevel> name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i0, 1, i1] flags: <all paths>

Additional information

Used terms: i0, 1, i1