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Proof step 25 from proof div-eq-same-01 (previous step)

0 = i1 * i0 + j0, j0 ≤ i1, 0 < i0, 0 ≤ j0, 0 < i1 ⊦ 0 = i1, i0 = 0, ~1 = i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 inst: name: zero-04 seq: ⊦ 0 < i ∧ 0 < j → 0 ≠ i + j subst: [j, i] → [j0, i1 * i0] flags: rewrite

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult Used terms: j0, i1 * i0