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Proof step 22 from proof le-abs-numerator (previous step)

j ≠ 0, 0 < j, 0 < ~(abs(i) / j) + ~ abs(i), ~ abs(i) < 0 ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 23:
⊦ 0 ≤ i ∧ 0 < j → i / j * j ≤ i
Proof step 24:
0 ≤ abs(i) ∧ 0 < j → abs(i) / j * j ≤ abs(i), j ≠ 0, 0 < j, 0 < ~(abs(i) / j) + ~ abs(i), ~ abs(i) < 0 ⊦

Rule argument

spec: int-div inst: name: ls-same-pos seq: ⊦ 0 ≤ i ∧ 0 < j → i / j * j ≤ i subst: [i, j] → [abs(i), j] flags: current, []

Additional information

Used terms: abs(i), j