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Proof step 5 from proof mult-03 (previous step)

1 < j, 0 < i0, i0 < j, 0 < i, 0 < j0, 0 < j, 0 ≤ j ⊦ ((i - 1) * j + (j - i0)) / (j0 * j) = (i - 1) / j0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: mult-02 seq: ⊦ 0 ≤ i0 ∧ i0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i * j + i0) / (j0 * j) = i / j0 subst: [j0, i0, j, i] → [j0, j - i0, j, i - 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ i * j + i = i * (j + 1); (s)% ⊦ i + (j - i) = j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i + 0 = i; (s)% ⊦ i - j < i0 ↔ i < j + i0; (s)% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i + j ≤ i ↔ j ≤ 0; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: j0, j - i0, j, i - 1