Theorems · Theorem · complex analysis
Real.cosh_pos
∀ (x : ℝ), 0 < Real.cosh x
Real.cosh is always positive
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Real.exp_posproof · cited by 169
- Real.coshstatement · cited by 119
- half_posproof · cited by 83
- add_posproof · cited by 28
- Real.cosh_eqproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Real.contDiff_arsinhproof · cited by 6
- Real.hasStrictDerivAt_arsinhproof · cited by 3
- Real.sinh_strictMonoproof · cited by 3
- UpperHalfPlane.cosh_half_distproof · cited by 3
- Real.cosh_arsinhproof · cited by 2
- Real.sinh_lt_coshproof · cited by 1
- Real.arcosh_coshproof · cited by 0