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Theorems · Theorem · order theory

le_of_forall_pos_lt_add

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] {a b : α},
  (∀ (ε : α), 0 < ε → a < b + ε) → a ≤ b
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
3 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
AddGroupLinearOrderAddLeftMono
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Around this declaration

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

gauge_add_le · cited by 4gauge_add_lesetOfPred_gauge_le_eq · cited by 3setOfPred_gauge_le_eqle_iff_forall_pos_lt_add · cited by 3le_iff_forall_pos_lt_addLinearOrder · cited by 8572LinearOrderAddGroup · cited by 4410AddGroupAddLeftMono · cited by 687AddLeftMonole_of_not_gt · cited by 430le_of_not_gtlt_irrefl · cited by 190lt_irrefladd_neg_cancel_left · cited by 76add_neg_cancel_leftlt_self_iff_false · cited by 41lt_self_iff_falselt_neg_add_iff_lt · cited by 1lt_neg_add_iff_ltle_of_forall_pos_lt_addCITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.