Formalizations Of Substitution Of Equals For Equals

Inference rule substitution of equals for equals has been formalized in terms of simple substitution which performs a replacement even though a free occurrence of a variable is captured contextual substitution which prevents such capture and func tion application We show that in connection with pure rst order predicate calculus the function application and no capture versions of the inference rule are the same and are weaker than the capture version We discuss the deductive apparatus needed for the no capture version to be as powerful as the capture version