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formal statement (Lean)
78theorem bigOmega_apply {n : ℕ} : bigOmega n = n.primeFactorsList.length := by
proof body
Term-mode proof.
79 simp only [bigOmega, ArithmeticFunction.cardFactors_apply]
80
81/-- Number of distinct prime divisors — ω(n). -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
-
bigOmega_one
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
-
bigOmega_prime_pow
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
-
liouville_one
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
depends on (6)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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-
bigOmega
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use