tenfold_times_D
plain-language theorem explainer
The identity 10 multiplied by 5 equals 50 underpins the factorization of ten-fold enumerations as twice a five-element structure within Recognition Science. Cross-domain researchers analyzing patterns such as 10 fingers or 10 decimal digits would reference this result to confirm scaling below the gap45+5 threshold. The proof relies on a direct decision procedure that verifies the natural-number arithmetic equality.
Claim. $10 × 5 = 50$
background
The module on ten-fold combinations asserts that many domains in Recognition Science enumerate to a cardinality of 10, factorized universally as 10 = 2 × 5 = 2D. Examples include 10 Hallmarks of Cancer as 5 clusters times 2, 10 fingers as 5 per hand times 2 hands, 10 decimal digits, and 10 d-block elements per period. This local theoretical setting provides structural claims with zero sorries or axioms.
proof idea
The proof is a one-line wrapper applying the decide tactic to resolve the arithmetic equality in natural numbers.
why it matters
This theorem supplies the basic arithmetic step for the ten-fold factorization 10 = 2 × D with D = 5 in the C17 wave of cross-domain combinations. It aligns with the framework's T7 eight-tick octave and the doubling for pairing 5-element structures. Although no immediate downstream theorems are listed, it closes a simple scaffolding step in the ten-fold module, supporting broader claims on enumerations like spinal levels and periodic table blocks.
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