Theorems · Theorem · order theory
EReal.exists_rat_btwn_of_lt
∀ {a b : EReal}, a < b → ∃ x, a < ↑↑x ∧ ↑↑x < b- Defined in
- Mathlib.Data.EReal.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- ERealstatement and proof · cited by 793
- LT.lt.transproof · cited by 370
- Real.toERealstatement and proof · cited by 303
- lt_irreflproof · cited by 190
- exists_rat_btwnproof · cited by 26
- not_top_ltproof · cited by 17
- EReal.coe_lt_topproof · cited by 17
- EReal.coe_lt_coe_iffproof · cited by 15
- EReal.bot_lt_coeproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- EReal.nhds_bot_basisproof · cited by 4
- EReal.nhds_top_basisproof · cited by 3
- EReal.lt_iff_exists_real_btwnproof · cited by 1
- EReal.denseRange_ratCastproof · cited by 0
- EReal.lt_iff_exists_rat_btwnproof · cited by 0