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Proof step 6 from proof div-mod (previous step)

0 < j, 0 ≤ i0, 0 ≤ i ⊦ 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

Proof step 7:
⊦ i | ~ j ↔ i | j
Proof step 8:
0 < j, 0 ≤ i, 0 ≤ i0 ⊦ j | i0 - i ↔ i % j = i0 % j, 0 < j ∧ 0 ≤ i0 ∧ i0 ≤ i

Rule argument

spec: <toplevel> name: div-neg seq: ⊦ i | ~ j ↔ i | j subst: [j, i] → [i0 - i, j] flags: <all paths>

Additional information

Used terms: i0 - i, j