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Proof step 18 from proof mod-zero-one (previous step)

(i % j + i0 % j) / j < j, (i % j + i0 % j) / j < 0, 0 < j, 0 ≤ i0, 0 ≤ i, (i % j + i0 % j) / j + 1 < j ⊦ (i % j + i0 % j) / j = 0, (i % j + i0 % j) / j = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: num-ls seq: ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0) subst: [j0, j, i] → [0, j, i % j + i0 % j] flags: rewrite, current

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: 0, j, i % j + i0 % j