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Proof step 7 from proof numle-07 (previous step)

⊦ j * i1 ≤ j ↔ ¬ (1 - i1) * j < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < i → (i * j ≤ i ↔ j ≤ 1)
Proof step 9:
⊦ j * i1 ≤ j ↔ ¬ (1 - i1) * j < 0, 0 < j

Rule argument

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

Additional information

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