It's definitely used by the people who design and build the electronic gadgets.
It's one of the fundamental rules they use in order to decide what to put inside
the gadget to make it work.
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Yes, the corollary to one theorem can be used to prove another theorem.
pythagoreans theorem was used to help build the pyramids
Both Thévenin's theorem and Norton's theorem are used to simplify circuits, for circuit analysis.
Any rational number can be used in the remainder theorem: 4 does not have a special role.
Pythagoras' theorem