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Proof step 3 from proof modzero-07 (previous step)

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

User applied rule apply lemma

And obtained the following new goals

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

Rule argument

spec: <toplevel> name: modlep seq: j * i ≤ j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [~ j, i, 0, j0]

Additional information

Used simplifier rules: ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: ~ j, i, 0, j0