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Proof step 10 from proof div-mod-eq (previous step)

i % j < 0, i % j < 0, i % j < 0 ⊦ j = 0, (i / j - 1) * j + i % j + j = i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-sub-split seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [j, 1, i / j] flags: rewrite

Additional information

Used simplifier rules: one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%divmod-rew: j ≠ 0 ⊦ i / j * j + i % j = i; from specification int-div%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, 1, i / j