Mathlib Map

Theorems · Theorem · commutative algebra

Nat.cast_ite

∀ {R : Type u_1} [inst : AddMonoidWithOne R] (P : Prop) [inst_1 : Decidable P] (m n : ℕ),
  ↑(if P then m else n) = if P then ↑m else ↑n
Defined in
Mathlib.Data.Nat.Cast.Defs
Cited by
16 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
AddMonoidWithOneDecidable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.coeff_natCast_ite · cited by 6Polynomial.coeff_natCast_…ArithmeticFunction.moebius_mul_coe_zeta · cited by 4ArithmeticFunction.moebiu…AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3AddSubgroup.leftCoset_cov…Subgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3Subgroup.leftCoset_cover_…ArithmeticFunction.LSeries_zeta_eq_riemannZeta · cited by 2ArithmeticFunction.LSerie…SkewPolynomial.coeff_natCast_ite · cited by 2SkewPolynomial.coeff_natC…Chebyshev.primeCounting_eq_theta_div_log_add_integral · cited by 2Chebyshev.primeCounting_e…Matrix.natCast_apply · cited by 1Matrix.natCast_applyAnalyticAt.exists_eventuallyEq_sum_add_pow_mul · cited by 1AnalyticAt.exists_eventua…MvPolynomial.coeff_sum_X_pow_of_fintype · cited by 1MvPolynomial.coeff_sum_X_…LieAlgebra.Basis.borelUpper_le_biSup · cited by 1Basis.borelUpper_le_biSupRootPairing.Base.cartanMatrix_map_abs · cited by 0Base.cartanMatrix_map_absModularForm.dimension_level_one · cited by 0ModularForm.dimension_lev…ArithmeticFunction.natCoe_one · cited by 0ArithmeticFunction.natCoe…ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors · cited by 0ArithmeticFunction.sum_di…AddMonoidWithOne · cited by 313AddMonoidWithOneNat.cast_iteCITED BYCITES

Cites1

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.