Explanation of eleven_check in IndisputableMonolith.CrossDomain.CardinalitySpectrum
(1) In plain English, the declaration asserts that the natural number 11 is neither equal to Dconfig (defined as 5) nor equal to eightTick (defined as 8). It performs a negative check excluding 11 from matching these two primitive RS generators.
(2) In Recognition Science, this matters because the cardinality spectrum is built from structured combinations of primitives such as Dspatial=3, Dconfig=5, eightTick=8, and gap45=45. The check positions 11 as requiring a less-clean decomposition (commented as 2³ + D − 2), reinforcing that the spectrum {2, 3, 4, 5, 6, 7, 8, 10, ...} arises from RS-specific operations rather than arbitrary integers.
(3) The formal statement (11 : ℕ) ≠ Dconfig ∧ (11 : ℕ) ≠ eightTick is read as the conjunction of two inequalities on natural numbers. The proof uses refine to split the conjunction and decide to computationally verify both sides from the definitions.
(4) Visible dependencies are the definitions Dconfig and eightTick in the same module, plus supporting equality theorems five_is_Dconfig and eight_is_2cube. The decide tactic resolves the equalities directly.
(5) This declaration does not prove any positive claim about 11 (e.g., a decomposition, membership in rsSpectrum, or physical interpretation), nor does it connect 11 to other RS modules or derive further spectrum properties.