IndisputableMonolith.Compat.Mathlib
The Compat.Mathlib module supplies targeted compatibility shims that align Mathlib's real-number lemmas with project conventions for division and positivity. Formalizers working on the Recognition Science codebase import it to prevent version-specific discrepancies in basic arithmetic. The module consists of one direct import of Mathlib plus four sibling lemmas that restate standard positivity and reciprocal rules in adjusted form.
claimCompatibility shims for real arithmetic: if $0 < x$ then $0 < x^{-1}$; if $0 ≤ x$ then $0 ≤ x^{-1}$; adjusted rule for $x^{-1} y = (x y)^{-1}$; and equivalence $0 < x$ iff $0 < x^{-1}$.
background
The module belongs to the Compat domain and serves as the Mathlib-facing layer for the IndisputableMonolith project. It performs a single import of Mathlib to expose real-number infrastructure while adding four adjusted lemmas that handle positivity of reciprocals and related multiplication identities. No new theoretical objects such as the J-cost function, defect distance, or phi-ladder are introduced here; the focus remains on stable access to foundational arithmetic for downstream modules.
proof idea
This is a definition module, no proofs. It opens with the import Mathlib statement and then declares the four sibling lemmas directly.
why it matters in Recognition Science
The module feeds the central Compat module, whose doc-comment states it supplies compatibility shims and project-wide constants to all downstream code. By stabilizing Mathlib access it supports the larger formalization effort that encodes the unified forcing chain and Recognition Composition Law without library friction.
scope and limits
- Does not introduce or prove any statements from the forcing chain T0-T8.
- Does not define J, phi, or any Recognition Science constants.
- Does not contain mass formulas or Berry threshold results.
- Limits scope to four basic reciprocal and positivity shims for reals.