Generate Isabelle or Coq proofs establishing partial or total correctness of imperative programs from code and formal specifications. Use when users need to: (1) Prove program correctness using Hoare logic, (2) Generate verification conditions from pre/postconditions, (3) Construct loop invariants and termination arguments, (4) Verify imperative programs with assignments, conditionals, and loops. Supports both partial correctness (if terminates, postcondition holds) and total correctness (terminates and postcondition holds) for both Isabelle/HOL and Coq.