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Proof step 25 from proof le-abs-numerator (previous step)

0 < j, abs(i) / j * j ≤ abs(i), abs(i) + abs(i) / j < 0 ⊦ j = 0, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0
Proof step 27:
¬(0 ≤ abs(i) ∧ 0 ≤ abs(i) / j), 0 < j, abs(i) / j * j ≤ abs(i), abs(i) + abs(i) / j < 0 ⊦ j = 0, i = 0

Rule argument

spec: int-abs inst: name: zero-gs seq: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0 subst: [j, i] → [abs(i) / j, abs(i)] flags: rewrite

Additional information

Used terms: abs(i) / j, abs(i)