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Proof step 4 from proof modlep-04 (previous step)

j * i + j0 ≤ j * i0 + j1, abs(j0) < j, abs(j1) < j, i0 < i, j * i0 + abs(j0) < j * i + abs(j1), j0 ≤ 0, j1 ≤ 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j < 0 → abs(j) = 0 - j
Proof step 6:
¬ j0 < 0, j * i + j0 ≤ j * i0 + j1, abs(j0) < j, abs(j1) < j, i0 < i, j * i0 + abs(j0) < j * i + abs(j1), j0 ≤ 0, j1 ≤ 0 ⊦
Proof step 9:
j0 < 0, j * i + j0 ≤ j * i0 + j1, 0 - j0 < j, abs(j1) < j, i0 < i, j * i0 + (0 - j0) < j * i + abs(j1), j0 ≤ 0, j1 ≤ 0 ⊦

Rule argument

spec: int-abs inst: name: Abs-neg seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0] flags: rewrite

Additional information

Used terms: j0