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Proof step 10 from proof numle-07 (previous step)

j ≤ 0 ⊦ j * i1 ≤ j ↔ ¬ i1 ≤ 0 ∨ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: le-same-02 seq: ⊦ i < 0 → (i * j ≤ i ↔ 1 ≤ j) subst: [j, i] → [i1, j] flags: rewrite, current

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: i1, j