Mathlib Map

Theorems · Theorem · field theory

Rat.cast_natCast

∀ {α : Type u_3} [inst : DivisionRing α] (n : ℕ), ↑↑n = ↑n
Defined in
Mathlib.Data.Rat.Cast.Defs
Cited by
67 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

exists_rat_btwn · cited by 26exists_rat_btwnPadic.norm_eq_zpow_neg_valuation · cited by 9Padic.norm_eq_zpow_neg_va…Padic.valuation_natCast · cited by 6Padic.valuation_natCastPadic.norm_p · cited by 5Padic.norm_pPadicInt.exists_pow_neg_lt_rat · cited by 4PadicInt.exists_pow_neg_l…Real.ofDigits_le_one · cited by 3Real.ofDigits_le_onePadic.valuation_ratCast · cited by 3Padic.valuation_ratCastReal.strictMono_eulerMascheroniSeq · cited by 3Real.strictMono_eulerMasc…Real.exists_isLUB · cited by 3Real.exists_isLUBAntitoneOn.integral_le_sum · cited by 3AntitoneOn.integral_le_sumPadicInt.isUnit_den · cited by 3PadicInt.isUnit_denNumberField.Units.dirichletUnitTheorem.seq_next · cited by 3dirichletUnitTheorem.seq_…AntitoneOn.sum_le_integral · cited by 2AntitoneOn.sum_le_integralComplex.isPrimitiveRoot_exp_rat · cited by 2Complex.isPrimitiveRoot_e…Real.deriv_Gamma_nat · cited by 2Real.deriv_Gamma_natDivisionRing · cited by 1062DivisionRingInt.cast_natCast · cited by 393Int.cast_natCastRat.cast_intCast · cited by 74Rat.cast_intCastRat.cast_natCastCITED BYCITES

Cites3

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

Cited by67

Results whose statement or proof uses this declaration.