Theorems · Theorem · field theory
Complex.ofReal_inj
∀ {z w : ℝ}, ↑z = ↑w ↔ z = w- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 1,654
- Complex.reproof · cited by 882
Cited by38
Results whose statement or proof uses this declaration.
- Real.rpow_mulproof · cited by 67
- Real.exp_ne_zeroproof · cited by 7
- Complex.ofReal_eq_zeroproof · cited by 6
- Complex.Gamma_ne_zeroproof · cited by 6
- Real.tanh_eq_sinh_div_coshproof · cited by 5
- Real.inv_one_add_tan_sqproof · cited by 4
- integral_rpowproof · cited by 4
- Real.cosh_negproof · cited by 3
- Real.cosh_sqproof · cited by 3
- tendsto_riemannZeta_sub_one_divproof · cited by 3
- Complex.meromorphicOrderAt_canonicalFactorproof · cited by 3
- Real.integral_rpow_mul_exp_neg_mul_Ioiproof · cited by 3