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Proof step 3 from proof est-4-big-01 (previous step)

j = 2 ∨ j = 3, (2 * i) / 3 < 2 * i % j, 0 < i, (2 * i) / 3 < j, j ≤ i, 2 < i, 2 * i < j * j, j ≤ 2 * i % j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: num-ls seq: ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0) subst: [j0, j, i] → [j, 3, 2 * i] flags: rewrite

Additional information

Used simplifier rules: zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, 3, 2 * i