Theorems · Theorem · complex analysis
Real.cosh_eq
∀ (x : ℝ), Real.cosh x = (Real.exp x + Real.exp (-x)) / 2
The definition of cosh in terms of exp.
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Complexproof · cited by 5,565
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Real.expstatement and proof · cited by 871
- Complex.expproof · cited by 612
- two_ne_zeroproof · cited by 251
- Complex.ofReal_negproof · cited by 130
- div_mul_cancel₀proof · cited by 122
- Real.coshstatement · cited by 119
- Complex.coshproof · cited by 118
- mul_twoproof · cited by 43
Cited by5
Results whose statement or proof uses this declaration.
- Real.cosh_posproof · cited by 7
- Real.cosh_arcoshproof · cited by 3
- Real.tanh_eqproof · cited by 3
- Real.cosh_logproof · cited by 1
- Real.exp_mul_le_cosh_add_mul_sinhproof · cited by 0