- #1

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I've used the following implication (conditional...whatever you want to call it) in a few proofs and was wondering if it's actually is true. I incorporated it into my proofs because it seemed to make obvious sense, but I'm not sure if I'm overlooking something- obvious or subtle.

[tex] T \subseteq S \Rightarrow \exists s' \in S \& \exists s'' \in S \ni [s' \leq t \leq s''], \forall t \in T [/tex].

English: If T is a subset of S, then there exists an s' in S and an s'' in S such that t is greater than or equal to s' and less than or equal to s'', for all t in T.

[tex] T \subseteq S \Rightarrow \exists s' \in S \& \exists s'' \in S \ni [s' \leq t \leq s''], \forall t \in T [/tex].

English: If T is a subset of S, then there exists an s' in S and an s'' in S such that t is greater than or equal to s' and less than or equal to s'', for all t in T.

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