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Proof step 3 from proof mult-05 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: mult-04 seq: ⊦ 0 < i0 ∧ i0 < j ∧ 0 < i ∧ 0 < j0 → (j * i - i0) / (j * j0) = (i - 1) / j0 subst: [i0, j, i, j0] → [i0, j, i, 1]

Additional information

Used simplifier rules: one: ⊦ i / 1 = i;% ⊦ 1 * i = i; (s)%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) Used terms: i0, j, i, 1