\[ \left( \forall x < t \right) \phi \: \text{means} \: \forall x \left( x < t \rightarrow \phi \right) \\ \left( \forall x \leq t \right) \phi \: \text{means} \: \forall x \left( \left( x < t \lor x ...(∀x<t)ϕmeans∀x(x<t→ϕ)(∀x≤t)ϕmeans∀x((x<t∨x=t)→ϕ)(∃x<t)ϕmeans∃x(x<t∧ϕ)(∃x≤t)ϕmeans∃x((x<t∨x=t)∧ϕ).