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Proof step 1 from proof abs-05 (conclusion)

⊦ i < 0 → abs(i + 1) = abs(i) - 1

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: Abs-neg: ⊦ j < 0 → abs(j) = 0 - j;%sub-sub: ⊦ i - j - i0 = i - j + i0;%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j;%abseq: ⊦ abs(i) + i = 0 ↔ i ≤ 0;%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;%le-def: ⊦ i ≤ j ↔ ¬ j < i;%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2