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Proof step 8 from proof div-mod (previous step)

0 < j, 0 ≤ i, 0 ≤ i0 ⊦ j | i0 - i ↔ i % j = i0 % j, 0 < j ∧ 0 ≤ i0 ∧ i0 ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: div-mod-01 seq: ⊦ 0 < j ∧ 0 ≤ i0 ∧ i0 ≤ i → (j | i - i0 ↔ i % j = i0 % j) subst: [i0, i, j] → [i, i0, j] flags: <all paths>

Additional information

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