Theorems · Theorem · field theory
Real.le_mk_of_forall_le
∀ {x : ℝ} {f : CauSeq ℚ abs}, (∃ i, ∀ j ≥ i, x ≤ ↑(↑f j)) → x ≤ Real.mk f- Defined in
- Mathlib.Data.Real.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- le_rflproof · cited by 1,558
- le_of_ltproof · cited by 1,175
- sub_eq_add_negproof · cited by 1,023
- add_le_addproof · cited by 666
- le_of_not_gtproof · cited by 430
- CauSeqstatement and proof · cited by 189
- IsCauSeqstatement · cited by 91
- half_posproof · cited by 83
- sub_add_sub_cancelproof · cited by 56
- not_lt_of_geproof · cited by 52
Cited by3
Results whose statement or proof uses this declaration.
- Real.exists_isLUBproof · cited by 3
- Real.mk_le_of_forall_leproof · cited by 2
- Real.mk_near_of_forall_nearproof · cited by 1