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Proof step 6 from proof nummult-ls-03 (previous step)

j + 1 - i1 = i, 0 < i, j < 0 ⊦ j < i * i0 ↔ i1 / i < i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j < 0, i1 ≤ j, i1 < 0 ⊦ j < (j + 1 - i1) * i0 ↔ i1 / (j + 1 - i1) < i0

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs