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Proof step 1 from proof modlsp-03 (conclusion)

j * i + j0 < j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ i ≤ i0

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0
Proof step 3:
j * i + j0 < j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ j * i + (j0 - j1) < j * i0 ∧ abs(j0 - j1) < j, i ≤ i0

Rule argument

spec: int-mult inst: name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i, j0 - j1, i0] flags: current, []

Additional information

Used terms: j, i, j0 - j1, i0