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Proof step 4 from proof abs-add-le-zero (previous step)

i < 0 ⊦ i = 0, i < abs(j)

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: j < 0

Additional information

Used simplifier rules: abs-08: ⊦ i < 0 → abs(i) = ~ i;%Minus-def: ⊦ ~ i = 0 - i;%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j;%Abs-pos: ⊦ ¬ j < 0 → abs(j) = j;%lf-08: ⊦ ¬ i < j ∧ ¬ i0 < i → ¬ i0 < j; (forward) from specification int-basic1%zero-01: ⊦ i < 0 ∧ j < 0 → i + j < 0; 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 formulas: j < 0