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Proof step 3 from proof mods-ls-04 (previous step)

j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i0, 0 ≤ i ⊦ i * j + j0 < i0 * j ↔ i < i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i < i0 ∧ 0 ≤ j0 ∧ j0 < j → i * j + j0 < i0 * j
Proof step 5:
0 < j, j0 < j, 0 ≤ i, 0 ≤ i0, 0 ≤ j0 ⊦ i * j + j0 < i0 * j ↔ i < i0, i < i0 ∧ 0 ≤ j0 ∧ j0 < j

Rule argument

spec: <toplevel> name: mods-ls-02 seq: ⊦ i < i0 ∧ 0 ≤ j0 ∧ j0 < j → i * j + j0 < i0 * j subst: [i0, j0, j, i] → [i0, j0, j, i] flags: <all paths>

Additional information

Used terms: i0, j0, j, i