Explain Proof

name explain-proof description Explain a proof or Lean code step-by-step for learning. Triggers on "explain", "how does this work", "teach me", "what does this mean", "walk me through", "I don't understand" Explain Proof Break down a proof into understandable pieces, explaining each step. Approach Start with the big picture Break into chunks Explain each chunk in plain language Connect to the formal notation Check understanding before continuing For Lean Code When explaining Lean tactics: Structure What we're proving: [goal in plain English]

Current state:

• We know: [hypotheses]
• We need: [goal]

This step: tactic_name

• What it does: [explanation]
• Why here: [reasoning]
• After this: [new goal/state] Common Tactics Explained Tactic Plain English intro h "Assume the hypothesis, call it h" apply f "Use theorem/function f" exact h "This is exactly what h says" rw [h] "Rewrite using equation h" simp "Simplify using known facts" ring "This follows by algebra" induction n "Prove for 0, then prove n→n+1" cases h "Consider all possibilities for h" constructor "Prove both parts separately" left / right "Prove one side of OR" obtain ⟨x, hx⟩ := h "Unpack: h gives us x with property hx" For Informal Proofs Structure The claim: [what we're proving]