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Proof step 37 from proof less-mult-div-01 (previous step)

i1 = 0, 0 < i0 * j + j0, 0 < j1, i1 < j, j0 < j, 0 < j, 0 < (j0 * i1) / j + i0 * i1, 0 < j0, 1 < j, 0 ≤ (j0 * i1) / j + i0 * i1, i0 * j + j0 ≤ (j0 * i1) / j + i0 * i1, 0 ≤ i0, 0 ≤ i1 ⊦ j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [i1, 0] flags: <all paths>

Additional information

Used simplifier rules: zero: j ≠ 0 ⊦ 0 / j = 0;% ⊦ i * 0 = 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%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) Used terms: i1, 0