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Proof step 11 from proof divide-by-10 (previous step)

i ≤ 65536, 0 ≤ i ⊦ (i * 52429) / 524288 = i / 10

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 12:
⊦ 0 ≤ i ∧ 0 < j → (∃ i0, j0. i = i0 * j + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 13:
0 ≤ i ∧ 0 < 10 → (∃ i0, j0. i = i0 * 10 + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < 10), i ≤ 65536, 0 ≤ i ⊦ (i * 52429) / 524288 = i / 10

Rule argument

spec: int-mult inst: name: exdivmodpos seq: ⊦ 0 ≤ i ∧ 0 < j → (∃ i0, j0. i = i0 * j + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j] → [i, 10] flags: []

Additional information

Used terms: i, 10