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Proof step 5 from proof zero-05 (previous step)

i < j, i / j < j, i / j < ~1, i / j < i, i < 0, i / j < 0, 0 < j, i + 1 < j ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: ls seq: 0 ≤ i0, 0 < i, 0 < j, i0 / i < i0 / j ⊦ j < i subst: [i0, i, j] → [~ i, 1, j] flags: current, []

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%one: ⊦ i / 1 = i;%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%neg-01: ⊦ ~ j < ~ i ↔ i < j; from specification int-abs Used terms: ~ i, 1, j