IndisputableMonolith.Compat.Mathlib
The Compat.Mathlib module supplies targeted compatibility shims for Mathlib arithmetic operations including reciprocal positivity and multiplication rules. It supports consistent behavior in the Recognition Science codebase for downstream modules. Researchers auditing the monolith import it to align basic lemmas with project conventions. The module contains only shim definitions with no complex proofs or theoretical derivations.
claimCompatibility shims for reciprocal rules: $x > 0 implies 1/x > 0$, $x ge 0 implies 1/x ge 0$, and $1/x cdot y$ identities, supplied as project shims.
background
The module imports Mathlib and defines shims for division and inversion. Sibling definitions include one_div_pos_of_pos' and related lemmas that restate standard positivity and multiplication properties for 1/x. The local setting is a compatibility layer that lets the Recognition Science monolith reuse Mathlib without friction while preserving project-wide arithmetic conventions.
proof idea
This is a definition module containing compatibility shims; no proofs are present.
why it matters in Recognition Science
It feeds IndisputableMonolith.Compat, the central compatibility import point whose doc-comment states that downstream modules gain access to shims and constants. The module therefore anchors the entire Compat domain and ensures Mathlib alignment for all later Recognition Science declarations.
scope and limits
- Does not introduce Recognition Science physics results or constants.
- Does not depend on the forcing chain, J-function, or phi-ladder.
- Does not prove new theorems beyond arithmetic shims.
- Limits scope to Mathlib compatibility only.