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Theorems · Theorem · order theory

le_min_iff

∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, c ≤ min a b ↔ c ≤ a ∧ c ≤ b
Defined in
Mathlib.Order.MinMax
Cited by
9 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

HasFPowerSeriesOnBall.add · cited by 5HasFPowerSeriesOnBall.addFilter.comap_abs_atTop · cited by 2Filter.comap_abs_atTopHasFPowerSeriesWithinOnBall.add · cited by 2HasFPowerSeriesWithinOnBa…FormalMultilinearSeries.radius_prod_eq_min · cited by 1FormalMultilinearSeries.r…List.prod_min_le · cited by 1List.prod_min_leList.le_minimum_of_forall_le · cited by 1List.le_minimum_of_forall…List.sum_min_le · cited by 1List.sum_min_leFinset.le_fold_min · cited by 0Finset.le_fold_minFilter.comap_mabs_atTop · cited by 0Filter.comap_mabs_atTopLinearOrder · cited by 8572LinearOrderle_inf_iff · cited by 48le_inf_iffle_min_iffCITED BYCITES

Cites2

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

Cited by9

Results whose statement or proof uses this declaration.