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Proof step 18 from proof div-shift-two (previous step)

j0 < j, 0 < j, 0 ≤ i0, 0 ≤ j0 ⊦ i0 = 1 + 2 * i0 / 2, j = 0, i0 * j + j0 < (1 + 2 * i0 / 2) * j

User applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 20:
i0 = i1 * 2 + j1, 0 < j, j0 < j, j1 < 2, 0 < 2, 0 ≤ j0, 0 ≤ i0, 0 ≤ j1, 0 ≤ i1 ⊦ i0 = 1 + 2 * i1, j = 0, i0 * j + j0 < (1 + 2 * i1) * j

Rule argument

spec: <toplevel> name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [i0, 2, i, j1] flags: <rotated> <all paths>

Additional information

Used terms: i0, 2, i, j1