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Proof step 9 from proof divides-abs-01 (previous step)

i < 0 ⊦ i0 = 0, ∃ i1. i * i1 + i * i0 = 0

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: ~ i0

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neg-03: ⊦ ~ i + i = 0; from specification int-abs%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