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 - 3. Cut Elimination - Gentzen's Hauptsatz: cuts can be eliminated - Subformula property: only subformulas appear - Usef…