invariants_and_monovariants

To prove termination using a monovariant in Lean 4, you identify a measurable property that strictly decreases across state transitions. This skill provides templates to formalize monotonic progress arguments for loop termination.

An invariant in state-transition systems is a property that must hold across all reachable states. By proving preservation, invariants constrain reachability and demonstrate that certain invalid states are unreachable.

Yes, you can use these Lean 4 templates for graph theory and unreachability proofs. They demonstrate how invariants constrain reachable states and provide worked examples for parity and state-transition reasoning.

The best way to set up formal proofs for loop termination is loading the invariant and monovariant templates into your Lean environment, then adapting them to specify measurable properties for your state space.

You need a monovariant instead of an invariant when proving termination and progress rather than state preservation. Monovariants imply termination by showing monotonic decrease, while invariants constrain reachable states.