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Proof step 12 from proof noeth-modlep (previous step)

j0 < j2, 0 < j2, i0 < i, 0 ≤ j0, ~1 * i0 - j0 * i0 ≤ (~1 - j0) * i + j0, (~1 * i0 - j0 * i0) + i0 ≤ i + (~1 - j0) * i + j0, ∀ 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 13:
⊦ (i - j) * j0 = i * j0 - j * j0
Proof step 14:
i0 < i, 0 < j2, j0 < j2, (~1 * i0 - j0 * i0) + i0 ≤ i + (~1 * i - j0 * i) + j0, ~1 * i0 - j0 * i0 ≤ (~1 * i - j0 * i) + 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: dist-sub-split seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [i, j0, ~1] flags: <all paths>

Additional information

Used terms: i, j0, ~1