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Induction over Term Values

Proposition: In order to prove F, it suffices to prove

(forall y in N: y=T => F)
where y does not occur freely in T or F.

Consequence: in order to prove

forall x0, ..., xn-1: F
we may prove
(forall x0, ..., xn-1,y in N: y=T => F)
where T is a term with free variables x0, ..., xn-1.

We introduce a variable over N to proceed by induction.

Author: Wolfgang Schreiner
Last Modification: November 24, 1999

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