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Proof step 16 from proof mod-zero-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 name: pls seq: i < j, i0 < j0 ⊦ i + i0 < j + j0 subst: [j0, j, i0, i] → [j, j, i % j, i0 % j] flags: <all paths>

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j;% ⊦ i + i = 2 * i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss) Used terms: j, j, i % j, i0 % j