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Theorems · Theorem · order theory

le_iff_forall_pos_lt_add

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] {a b : α},
  a ≤ b ↔ ∀ (ε : α), 0 < ε → a < b + ε
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
3 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
AddGroupLinearOrderAddLeftMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Real.sInf_le_iff · cited by 0Real.sInf_le_iffReal.le_sSup_iff · cited by 0Real.le_sSup_iffschnirelmannDensity_le_iff_forall · cited by 0schnirelmannDensity_le_if…LinearOrder · cited by 8572LinearOrderAddGroup · cited by 4410AddGroupAddLeftMono · cited by 687AddLeftMonolt_add_of_le_of_pos · cited by 11lt_add_of_le_of_posle_of_forall_pos_lt_add · cited by 3le_of_forall_pos_lt_addle_iff_forall_pos_lt_addCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.