Replacement Rules: The Concept
This video presents the same text shown beside it, spoken and on screen. It adds nothing the text does not say.
State
Replacement rules are equivalences: they swap interchangeable forms, in either direction, applied to whole lines or any part of a line.
Show
Inference rules are one-way and whole-line; replacement rules are two-way and reach inside formulas.
Watch for
This difference in reach is exactly why the system needs both kinds. The "::" in what follows means "replace either side with the other."