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Proof step 18 from proof noeth-modlep (previous step)

j0 < j2, 0 < j2, i0 < i, i * j0 < i0 * j0 + j0, 0 ≤ j0, i + j0 * i ≤ j0 * i0 + i0 + j0, j0 * i + i + i0 - i0 + j0 * i0 ≤ j0 + i, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ ~1 = j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ (* i0) * i + i = (i0 + 1) * i
Proof step 20:
i * j0 < (i0 + 1) * j0, i0 < i, 0 < j2, j0 < j2, j0 * i + i + i0 - i0 + j0 * i0 ≤ j0 + i, i + j0 * i ≤ j0 * i0 + i0 + j0, 0 ≤ j0, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ ~1 = j0

Rule argument

spec: <toplevel> name: numsucc seq: ⊦ (* i0) * i + i = (i0 + 1) * i subst: [i, i0] → [j0, i0] flags: <all paths>

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; Used terms: j0, i0