local_to_global_hasse_principle

What problem does it solve?

Prove a global existence result by first establishing existence at all local completions (p-adic and real), then applying the Hasse-Minkowski theorem or analogous local-global principle to lift to the integers or rationals.

Core Features & Use Cases

• Local-to-global reasoning for polynomial solvability: verify real and p-adic solvability and then deduce a global witness using Hasse-type principles.
• Lean 4 formalization templates: encode local checks, Hensel lifting steps, and construction of a global solution within Lean 4 using Mathlib.
• Worked scenarios: applies to quadratic forms and related algebraic structures where local data governs global solvability, with descent-style strategies for lifting to ℚ.

Quick Start

Apply the Hasse principle by verifying real and p-adic solvability for a quadratic form over ℚ, then deduce a global rational solution.