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Theorems · Theorem · real analysis

CauSeq.le_of_eq_of_le

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] {f g h : CauSeq α abs},
  f ≈ g → g ≤ h → f ≤ h
Defined in
Mathlib.Algebra.Order.CauSeq.Basic
Cited by
2 results in Mathlib
Foundations
Depth 69 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_inf · cited by 0CauSeq.le_infLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingabs · cited by 1814absCauSeq · cited by 189CauSeqCauSeq.lt_of_eq_of_lt · cited by 2CauSeq.lt_of_eq_of_ltCauSeq.le_of_eq_of_leCITED BYCITES

Cites6

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.