Theorems · Theorem · order theory
le_of_forall_lt
∀ {α : Type u_2} [inst : LinearOrder α] {a b : α}, (∀ c < a, c < b) → a ≤ b- Defined in
- Mathlib.Order.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- le_of_not_gtproof · cited by 430
- lt_irreflproof · cited by 190
Cited by25
Results whose statement or proof uses this declaration.
- Cardinal.mul_eq_selfproof · cited by 13
- Cardinal.ord_aleph0proof · cited by 9
- Cardinal.lift_ordproof · cited by 8
- Cardinal.ord_univproof · cited by 8
- MeasureTheory.Measure.InnerRegularWRT.measure_eq_iSupproof · cited by 7
- Antitone.map_limsSup_of_continuousAtproof · cited by 6
- forall_lt_iff_leproof · cited by 5
- Ordinal.IsFundamentalSeq.iSup_add_one_eqproof · cited by 3
- Order.enum_le_of_forall_ltproof · cited by 3
- eq_of_forall_lt_iffproof · cited by 3
- Order.IsSuccPrelimit.isLUB_Iioproof · cited by 3
- Ordinal.natCast_add_omega0proof · cited by 3