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Proof step 1 from proof est-4-big-01 (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
(2 * i) / 3 < 2 * i % j, 0 < i, (2 * i) / 3 < j, j ≤ i, 2 < i, 2 * i < j * j, j ≤ 2 * i % j ⊦

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%less-mult-div-01: ⊦ 0 < i ∧ 0 < j ∧ 0 < j1 ∧ i1 < j → (i * i1) / j < i; from specification int-div%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs