IndisputableMonolith.Foundation.UniversalForcing.Invariance.TwoCases
The module establishes that continuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic. Researchers working on the Universal Forcing theorem would cite this equivalence when unifying realizations. The argument proceeds by importing the continuous realization from the positive-ratio comparison wrapper and the discrete Boolean realization, then connecting them via their canonical equivalence.
claimContinuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic.
background
The module resides in the Foundation.UniversalForcing.Invariance namespace and imports two upstream modules. ContinuousRealization re-exports the wrapper LogicRealization.ofPositiveRatioComparison under the Universal Forcing namespace. DiscreteRealization re-exports the Boolean/propositional realization. This supplies the two arithmetic cases whose invariance is asserted in the module doc-comment.
proof idea
The module imports the continuous and discrete realization modules. It structures the argument around the sibling theorem that directly equates the two realizations. No additional hypotheses are introduced beyond the imported re-exports.
why it matters in Recognition Science
This module feeds the AxiomAudit, which supplies the reproducible theorem surface for the Universal Forcing Lean program, and the general Universal theorem stating that every Law-of-Logic realization carries canonically equivalent forced arithmetic. It supplies the two-cases step required for invariance under the forcing chain.
scope and limits
- Does not address realizations outside positive-ratio and Boolean arithmetic.
- Does not introduce new constants, dimensions, or forcing steps.
- Does not claim equivalence for non-arithmetic structures.