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Proof step 12 from proof nummult-ls (previous step)

j0 < i, 0 < i, i2 < i0, 0 ≤ j0, i * i0 ≤ i2 * i + j0, ~1 ≤ i2 * i + j0, 0 ≤ i + i2 * i + j0 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modlep seq: j * i ≤ j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [i, i0, i2, j0]

Additional information

Used simplifier rules: ⊦ i < j → (j ≤ i ↔ false); (as)%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, i0, i2, j0