ten_eq_two_D
plain-language theorem explainer
The arithmetic identity ten equals two times five supplies the universal factorization for all ten-fold enumerations across Recognition Science domains. Cross-domain researchers cite it when building certificates that collect structures such as fingers, decimal digits, lumbar-sacral levels, and d-block elements under a common cardinality. The proof is a direct decision procedure that verifies the equality in the natural numbers with no additional lemmas.
Claim. In the natural numbers, the cardinality ten factors as two multiplied by five: $10 = 2 × 5$.
background
The module C17 collects ten-fold structures from multiple Recognition Science domains and shows each admits the factorization 10 = 2 × 5. The doubling represents the pairing of a five-element set with an orientation, polarity, or alternation. Concrete instances include ten fingers (five per hand across two hands), ten decimal digits, ten lumbar plus sacral spinal levels, and ten d-block elements per period. The local setting is the cross-domain claim that all such enumerations share this 2 × 5 splitting and can be assembled into a single certificate.
proof idea
The proof is a one-line wrapper that applies the decide tactic to confirm the arithmetic equality directly.
why it matters
This theorem supplies the ten_factoring field inside the TenFoldCombinationsCert definition, which aggregates the individual cardinality proofs for fingers, digits, lumbar-sacral vertebrae, and d-block elements. It realizes the structural claim of module C17 that ten equals two times five across domains, consistent with the framework's use of self-similar factorizations and the eight-tick octave. No open questions attach to this basic identity.
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