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Theorems · Theorem · order theory

forall_lt_iff_le

∀ {α : Type u_2} [inst : LinearOrder α] {a b : α}, (∀ ⦃c : α⦄, c < a → c < b) ↔ a ≤ b
Defined in
Mathlib.Order.Basic
Cited by
5 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
LinearOrder
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Around this declaration

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

Filter.le_limsup_iff · cited by 10Filter.le_limsup_iffFilter.le_limsup_iff' · cited by 3Filter.le_limsup_iff'Sion.minimax · cited by 2Sion.minimaxFinset.kruskal_katona_lovasz_form · cited by 1Finset.kruskal_katona_lov…Fin.coe_orderIso_apply · cited by 0Fin.coe_orderIso_applyLinearOrder · cited by 8572LinearOrderlt_of_lt_of_le · cited by 438lt_of_lt_of_lele_of_forall_lt · cited by 25le_of_forall_ltforall_lt_iff_leCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.