Proof Theory

When to Use

Use this skill when working on proof-theory problems in mathematical logic.

Decision Tree

1. Proof Strategy Selection

   • Direct proof: assume premises, derive conclusion
   • Proof by contradiction: assume negation, derive false
   • Proof by cases: split on disjunction
   • Induction: base case + inductive step

2. Structural Induction

   • Define well-founded ordering on structures
   • Base: prove for minimal elements
   • Step: assume for smaller, prove for current