Theorems · Theorem · field theory
Real.mk_le_of_forall_le
∀ {f : CauSeq ℚ abs} {x : ℝ}, (∃ i, ∀ j ≥ i, ↑(↑f j) ≤ x) → Real.mk f ≤ x- Defined in
- Mathlib.Data.Real.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- absstatement and proof · cited by 1,814
- CauSeqstatement and proof · cited by 189
- IsCauSeqstatement · cited by 91
- neg_le_neg_iffproof · cited by 57
- Rat.cast_negproof · cited by 25
- Real.mkstatement · cited by 19
- Real.le_mk_of_forall_leproof · cited by 3
- Real.mk_negproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.exists_isLUBproof · cited by 3
- Real.mk_near_of_forall_nearproof · cited by 1