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Proof step 31 from proof div-eq-same-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i + 0 = 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 = 0 ↔ i = 0 ∨ j = 0; (ws) Used terms: j0, i0 * i