One-preserving Boolean function
= One-preserving Boolean function
{title2=$f(1,\ldots,1)=1$}
A <Boolean function> satisfying the displayed condition. Composition of <one-preserving Boolean functions> is one-preserving, since each inner output is one on an all-one input. Consequently <structural induction> shows that a variable-built <propositional formula> using only one-preserving <logical connectives>, such as $\land,\lor,\to$, is true under the all-one <Boolean valuation>.