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Proof step 21 from proof mod-zero-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 inst: name: pls-01 seq: ¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0 subst: [j, i] → [i0 % j, i % j] flags: rewrite

Additional information

Used simplifier rules: mod-zero-01: ⊦ 0 < j ∧ 0 ≤ i → ¬ i % j < 0; Used terms: i0 % j, i % j