Theorems · Theorem · field theory
Complex.ofReal_sub
∀ (r s : ℝ), ↑(r - s) = ↑r - ↑s
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- sub_selfproof · cited by 996
- Complex.ext_iffproof · cited by 20
Cited by63
Results whose statement or proof uses this declaration.
- Real.cos_addproof · cited by 8
- Real.sinh_eqproof · cited by 5
- Real.cos_two_mulproof · cited by 4
- ProbabilityTheory.complexMGF_id_gaussianRealproof · cited by 3
- Circle.exp_injOn_of_forall_sub_mem_Iooproof · cited by 3
- UpperHalfPlane.hasStrictDerivAt_smulproof · cited by 3
- Complex.IsExpCmpFilter.isLittleO_cpow_mul_expproof · cited by 3
- Complex.arg_expproof · cited by 3
- Real.sin_sub_sinproof · cited by 2
- Complex.norm_eq_one_iff'proof · cited by 2
- Real.cosh_sub_sinhproof · cited by 2
- Real.cos_boundproof · cited by 2