Theorems · Definition · complex analysis
Real.tanh
ℝ → ℝ
The real hyperbolic tangent function, defined as the real part of the complex hyperbolic tangent
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 144 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
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Complex.tanhproof · cited by 20
Cited by20
Results whose statement or proof uses this declaration.
- Real.tanhPartialEquivproof · cited by 6
- Real.tanh_eq_sinh_div_coshstatement · cited by 5
- Real.tanh_eqstatement · cited by 3
- Real.tanh_lt_onestatement · cited by 1
- Real.abs_tanh_lt_onestatement · cited by 1
- Real.neg_one_lt_tanhstatement · cited by 1
- Complex.ofReal_tanhstatement · cited by 1
- Real.tanh_arsinhstatement · cited by 0
- Real.tanh_artanhstatement · cited by 0
- Real.tanh_bijOnstatement · cited by 0
- Real.tanh_injectivestatement · cited by 0
- Real.tanh_negstatement · cited by 0