proof of the well-founded induction principle
This proof is very similar to the proof of the transfinite induction theorem. Suppose is defined for a well-founded set , and suppose is not true for every . Assume further that satisfies requirements 1 and 2 of the statement. Since is a well-founded relation, the set has an minimal element . This element is either an minimal element of itself, in which case condition 1 is violated, or it has predessors. In this case, we have by minimality for every such that , and by condition 2, is true, contradiction.
|Title||proof of the well-founded induction principle|
|Date of creation||2013-03-22 12:42:20|
|Last modified on||2013-03-22 12:42:20|
|Last modified by||jihemme (316)|