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Proof step 3 from proof mod-twoodd-02 (previous step)

j % (2 * i) = 1, 0 < i, 0 ≤ j ⊦ j % 2 = 1

User applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used simplifier rules: mod-mult-02: 0 ≠ j, i0 ≠ 0 ⊦ (i0 * i) % (i0 * j) = i % j * i0;% ⊦ i ≠ 1 ∧ 0 ≤ i → (i < 2 ↔ i = 0); (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = j; (ws)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: j, 2, i0, j0