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First-order formula

Quantifier order

{title2=$\exists y\forall x\,R(x,y)$}

One element that satisfies a relation simultaneously for every quantified input. A uniform witness also proves the corresponding pointwise statement, because it may be chosen for each particular input.


Uniform witness

Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 8 / b / Solution

Pointwise witness

Uniform witness ( $\exists y \forall x R (x, y)$ )

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Uniform witness (∃y∀xR(x,y))

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Uniform witness ( $\exists y \forall x R (x, y)$ )

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