vacuously true
vacuously satisfied
vacuously defined
vacuously holds
vacuously satisfies
vacuously empty
vacuously stated
vacuously assumed
vacuously implies
vacuously meets
the statement is vacuously true because the condition is never met.
the theorem vacuously holds for the empty set.
the hypothesis vacuously satisfies the requirement.
the condition is vacuously satisfied in this case.
the result is vacuously true given the constraints.
the statement vacuously becomes true when x is zero.
the definition vacuously includes the trivial case.
the property vacuously applies to a single element.
the inequality is vacuously satisfied when n is negative.
the condition vacuously holds for the base case.
the statement vacuously proves the point.
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