📄️ Multi-step Proofs
Often a theorem isn't so obvious that you just realize it's true in a single flash of insight. Instead, you think about it, and you start to see a sequence of things that follow from the premises. Your thought process goes:
📄️ Indirect Proofs
Sometimes a proof doesn't fit naturally into a format where each step follows naturally from the steps before it. For example, we might want an "indirect proof" - where you assume something, then prove a contradiction, and thus conclude that your initial assumption was false.
📄️ Induction
Induction is the soul of the natural numbers. You prove something is true for zero, and that whenever it's true for one number, it's true for the next one. And there you go, it's true for all natural numbers.
📄️ The Acorn Master Plan
Acorn is a theorem prover. It checks that a mathematical proof is perfectly correct.