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Proof step 6 from proof div-add-nosucc (previous step)

j0 * j + j = i0 + 1, 0 < j, 1 < j, 0 ≤ j0 ⊦ j = 0, i0 / j = j0

User applied rule insert lemma

And obtained the following new goals

Proof step 7:
⊦ i0 % j = 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j
Proof step 8:
(j * j0) % j = 0 ∧ 0 ≤ j - 1 ∧ 0 ≤ j * j0 ∧ 0 < j → ((j - 1) + j * j0) / j = (j - 1) / j + (j * j0) / j, j0 * j + j = i0 + 1, 0 < j, 1 < j, 0 ≤ j0 ⊦ j = 0, i0 / j = j0

Rule argument

spec: inst: name: div-add-pos seq: ⊦ i0 % j = 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j subst: [i0, j, i] → [j * j0, j, j - 1] flags: current, []

Additional information

Used terms: j * j0, j, j - 1