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Proof step 2 from proof ls-same-pos-01 (previous step)

(i / j + 1) * j ≤ i, 0 ≤ i, 0 < j ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i ∧ 0 < j → i / j * j ≤ i ∧ i < (i / j)+1 * j

Rule argument

spec: int-div inst: name: Div-def seq: ⊦ 0 ≤ i ∧ 0 < j → i / j * j ≤ i ∧ i < (i / j)+1 * j subst: [i, j] → [i, j] flags: current, []

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i, j