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Theorems · Theorem · real analysis

CauSeq.lt_of_lt_of_eq

∀ {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 68 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.le_of_le_of_eq · cited by 2CauSeq.le_of_le_of_eqCauSeq.lt_lim · cited by 0CauSeq.lt_limLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingabs · cited by 1814absneg_sub · cited by 272neg_subCauSeq · cited by 189CauSeqsub_add_sub_cancel' · cited by 18sub_add_sub_cancel'CauSeq.Pos · cited by 13CauSeq.PosCauSeq.neg_limZero · cited by 5CauSeq.neg_limZeroCauSeq.pos_add_limZero · cited by 2CauSeq.pos_add_limZeroCauSeq.lt_of_lt_of_eqCITED BYCITES

Cites10

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.