fixed_point_arguments

What problem does it solve?

Prove existence of x* such that f(x*) = x* for functions f : X → X using Brouwer's, Banach's, or Tarski's fixed-point theorems, based on the nature of the underlying space.

Core Features & Use Cases

• Theorem selection: Choose Banach, Brouwer, or Tarski according to the space (complete metric space, compact convex set, or complete lattice) to guarantee existence of fixed points.
• Constructive/Non-constructive outcomes: Obtain constructive iterations via Banach (when contraction) or non-constructive existence via Brouwer; leverage monotone operators via Tarski.
• Use Case: Prove that a given iterative map has a fixed point, enabling formal verification, analysis proofs, or Lean-based developments of fixed-point arguments.

Quick Start

State the function f and the applicable space X, then apply the appropriate fixed-point theorem to establish the existence of x* with f(x*) = x*.