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Proof step 2 from proof bint-div2 (previous step)

j0 ≤ j, ~2147483648 ≤ j, j ≤ 2147483647, 0 < j0, 0 < j, j0 ≤ 2147483647 ⊦ (j0 / 2)∈bint

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: bint-num-04 seq: ~2147483648 ≤ i, i < 2147483648 ⊦ (* i) ∈bint subst: [i] → [j0 / 2] flags: rewrite, current

Additional information

Used simplifier rules: inbint: ⊦ i ∈bint ↔ ~2147483648 ≤ i ∧ i ≤ 2147483647;%bint-num-02: j ≤ ~2147483648 ⊦ i < (* j) → ¬ i ∈bint;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%div-ls-same: ⊦ 0 < j → (i < i / j ↔ i < 0 ∧ 1 < j); from specification int-div%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%div-ls-zero: 0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0; from specification int-div%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%zero-gels-02: ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j0 / 2