Theorems · Definition · special functions
Real.expOrderIso
ℝ ≃o ↑(Set.Ioi 0)
Real.exp as an order isomorphism between ℝ and (0, +∞).
- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.Elemstatement · cited by 7,166
- Set.Ioistatement and proof · cited by 1,463
- OrderIsostatement · cited by 874
- Real.expproof · cited by 871
- Set.codRestrictproof · cited by 48
- StrictMono.orderIsoOfSurjectiveproof · cited by 8
Cited by13
Results whose statement or proof uses this declaration.
- Real.logproof · cited by 939
- Real.continuousOn_logproof · cited by 17
- Real.exp_log_eq_absproof · cited by 7
- Real.coe_comp_expOrderIsostatement · cited by 5
- Real.log_of_ne_zerostatement · cited by 3
- Real.isOpenEmbedding_expproof · cited by 2
- Real.map_exp_atBotproof · cited by 2
- Real.map_exp_atTopproof · cited by 2
- Real.coe_expOrderIso_applystatement · cited by 1
- Real.image_exp_Iicproof · cited by 1
- Real.image_exp_Iioproof · cited by 1
- Real.range_expproof · cited by 1