The author takes a deep dive into the world of proving theorems with great detail to convince a computer proof assistant of their correctness. By teaching students to write proofs manually, the author aims to expand their understanding of formal definitions and proof possibilities. A critical analysis of proof by induction reveals the rigid constraints students face, prompting a discussion on proof principles and induction hypotheses. The post delves into the proof that the square root of 2 is irrational, distinguishing between negation and contradiction proofs. The concept of infinite descent proof and its relationship to well-foundedness theory are explored, providing a new perspective on induction and proof principles.
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