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Proof step 11 from proof nummult-le-02 (previous step)

i2 < i0, 0 ≤ j0, j0 < i, ~1 ≤ i2 * i + j0, 0 < i, ~1 ≤ i2, 0 ≤ i + i2 * i + j0 ⊦ i2 * i + j0 < i * i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i * i0 ≤ i2 * i + j0, 0 ≤ i + i2 * i + j0, ~1 ≤ i2, 0 < i, ~1 ≤ i2 * i + j0, j0 < i, 0 ≤ j0, i2 < i0, 0 ≤ i0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs