Proofsstructured

Proofsstructured is a design approach for mathematical proof and formal verification that emphasizes building arguments as structured, modular components with explicit dependencies and labeled steps. In this paradigm, complex proofs are decomposed into small, reusable units whose input hypotheses and resulting conclusions are named and tracked throughout the argument. The representation is intended to be both human-readable and amenable to machine checking, often by modeling the proof as a directed acyclic graph of steps or as structured scripts in formal proof systems.

Core features include modular decomposition of arguments into lemmas or blocks, explicit labeling of hypotheses and conclusions, and a clear accounting of dependencies between steps. Proofsstructured promotes traceability, enabling readers to see exactly which earlier results support a given claim. It is commonly paired with formal languages or proof assistants, where structured blocks map to code or commands, and where dependency graphs can be inspected or partially automated.

Relation to existing concepts is close to structured proofs in traditional logic, sequent calculus, or proof nets, but with a focus on explicit dependency tracking and machine verification. In practice, it aligns with proof engineering practices used in Coq, Lean, Isabelle, or other formal verification environments, while remaining applicable to conventional mathematical writing. Education and collaborative work benefit from improved readability, version control compatibility, and easier error localization.

Applications span pure mathematics, computer science, and formal methods, including algorithm correctness, software verification, and teaching proof design. A simple example shows a proofstructured approach: to prove that the sum of two even numbers is even, you define Lemma L1: an even number a equals 2k; Lemma L2: an even number b equals 2m. Theorem T follows since a+b = 2(k+m). Each lemma and the theorem is a labeled node with explicit dependencies, enabling straightforward verification and reuse.