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Proof step 10 from proof auxexdivmod (previous step)

~1 ≤ i2, i < i0 * j + i2 * j + j, i0 * j ≤ i, 0 < i0 * j + i2 * j + j, 0 ≤ i, 0 < j, 0 ≤ i0, 0 < i2 * j + j ⊦ 0 ≤ i2, ∃ i1. i1 * j ≤ i ∧ i < i1 * j + j ∧ 0 ≤ i1, i0 * j + i2 * j ≤ i ∧ 0 ≤ i0 + i2

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: i0

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%mone-08: ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i0