IndisputableMonolith.Compat.FunctionIterate
The FunctionIterate module supplies a compatibility shim that defines iteration of a function f for n steps starting from an initial value a. It is imported by the central Compat module to give the rest of the Recognition Science codebase a uniform iterate operation. The module wraps Mathlib iteration so that higher-level constructions can treat function iteration as a stable primitive without depending on library internals.
claimThe module exports the operation iterate(f, n, a) that returns the value obtained by applying the function f exactly n times to the starting point a.
background
This module sits in the Compat domain and imports only Mathlib. Its single definition provides a project-wide shim for iterated function application, a standard construct used when building recursive or compositional objects. The surrounding Compat layer collects such shims so that downstream files can import a single file and obtain consistent constants and operations.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module is imported by IndisputableMonolith.Compat, the central compatibility layer that supplies shims and constants for the project. It therefore supports any construction that relies on repeated function application, including steps in the unified forcing chain.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not introduce Recognition Science specific constants, relations, or forcing-chain objects.
- Provides only the iterate definition as a compatibility shim.