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I would call item (1) the pseudowork/pseudoKE theorem.
I recognize that
delta pseudoKE = pseudowork
is a valid expression, but it needs to be stated
properly. IMHO it would be a reeeeeally sloppy
shorthand to call the LHS "the" KE or to call the
RHS "the" work. I shudder to think of it. It's
like nails screeching on the chalkboard.