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Proof step 2 from proof diveq-pos (previous step)

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

User applied rule insert lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used terms: i0 * j + j0, j