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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: <toplevel> name: le-same-02 seq: ⊦ i < 0 → (i * j ≤ i ↔ 1 ≤ j) subst: [j, i] → [i1, j] flags: <all paths>

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i ≤ j → (j < i ↔ false); (as)% ⊦ i < j ↔ ¬ j ≤ i; (ss)%lf-03: ⊦ i < j ∧ i = i0 → i0 < j; (forward) from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss) Used terms: i1, j