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Construction from Sets

0 := 0;
x' := x union {x}.

Proof of first Peano law:

We prove forall x: x' != 0. Take arbitrary x. By definition of 0 and ', we have to prove

x union {x} != 0

which is true because x in (x union {x}) but x not  in 0.

Proof of second Peano law: see lecture notes.

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

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