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Theorems · Theorem · real analysis

CauSeq.const_le

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] {x y : α},
  CauSeq.const abs x ≤ CauSeq.const abs y ↔ x ≤ y
Defined in
Mathlib.Algebra.Order.CauSeq.Basic
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CauSeq.lim_le · cited by 4CauSeq.lim_leCauSeq.le_lim · cited by 1CauSeq.le_limLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingabs · cited by 1814absCauSeq · cited by 189CauSeqCauSeq.const · cited by 58CauSeq.constle_iff_lt_or_eq · cited by 26le_iff_lt_or_eqCauSeq.const_lt · cited by 5CauSeq.const_ltCauSeq.const_equiv · cited by 3CauSeq.const_equivCauSeq.const_leCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.