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Lemma: The Proving Principle by Transfinite Induction
The proving principle by transfinite induction is a valid logical argument in first order predicate logic^{1}. It consists of:
 the base case premise: $p(\alpha)$ for some ordinal number $\alpha,$
 the induction step premise: prove that $p(\beta)$ is true assuming that $p(\alpha)$ is true for all $\alpha\subset \beta,$
 the conclusion: $p(\beta)$ is true for all ordinal numbers $\beta$ greater than or equal the base case $\alpha.$
Table of Contents
Proofs: 1
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References
Bibliography
 Toenniessen, Fridtjof: "Topologie", Springer, 2017
Footnotes