Theorems · Theorem · field theory
Real.exists_isLUB
∀ {s : Set ℝ}, s.Nonempty → BddAbove s → ∃ x, IsLUB s x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Set.Nonemptystatement and proof · cited by 2,627
- LT.lt.leproof · cited by 2,189
- absproof · cited by 1,814
- le_rflproof · cited by 1,558
- LT.lt.ne'proof · cited by 1,417
- le_transproof · cited by 985
- LT.lt.trans_leproof · cited by 678
- BddAbovestatement and proof · cited by 620
Cited by3
Results whose statement or proof uses this declaration.
- Real.isLUB_sSupproof · cited by 1
- Real.sSup_defstatement · cited by 0
- Real.exists_isGLBproof · cited by 0