Theorems · Theorem · real analysis
Real.norm_exp_I_mul_ofReal_sub_one_le
∀ {x : ℝ}, ‖Complex.exp (Complex.I * ↑x) - 1‖ ≤ ‖x‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Norm.normstatement and proof · cited by 5,413
- absproof · cited by 1,814
- Complex.ofRealstatement · cited by 1,654
- Complex.Istatement · cited by 866
- Complex.expstatement · cited by 612
- Real.sinproof · cited by 389
- norm_mulproof · cited by 171
- zero_lt_twoproof · cited by 124
- Real.norm_eq_absproof · cited by 88
- abs_divproof · cited by 38
Cited by1
Results whose statement or proof uses this declaration.
- Real.enorm_exp_I_mul_ofReal_sub_one_leproof · cited by 1