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Proof step 8 from proof div-elim-posneg (previous step)

j < 0, j1 + j < 0, 0 ≤ j1, 0 ≤ i1 * j + j1 ⊦ i1 ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ≤ j ↔ ¬ j < i

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [0, i1] flags: <all paths>

Additional information

Used simplifier rules: add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ j0 + j < 0 ∧ j < 0 ∧ 0 < i → ¬ 0 ≤ i * j + j0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 0, i1