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Proof step 2 from proof estimate-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ 0 < i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 4:
i * i0 = i1 * j + j1 ∧ 0 ≤ j1 ∧ j1 < j ∧ 0 < i * i0, j < i, j0 < i0, i1 ≤ j0, 0 < i0, 0 < j, 0 < i, 1 < i, i1 < i0 ⊦

Rule argument

spec: int-div inst: name: div-elim seq: ⊦ 0 < j ∧ 0 < i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [i * i0, j, i1, j1] flags: rewrite, current

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 Used terms: i * i0, j, i1, j1