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Proof step 2 from proof div-ls-01 (previous step)

i0 % j = 0, 0 < j, i < i0, 0 ≤ i ⊦ i / j < i0 / j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
j0 ≤ i / j, i < i0, i0 % j = 0, 0 < j, 0 ≤ i ⊦ j0 < i0 / j

Rule argument

spec: <toplevel> name: div-ls seq: j0 ≤ i / j, i < i0, i0 % j = 0, 0 < j, 0 ≤ i ⊦ j0 < i0 / j subst: [j0, i, j, i0] → [i / j, i, j, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ i; (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: i / j, i, j, i0