Theorems · Theorem · order theory
le_max_iff
∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a ≤ max b c ↔ a ≤ b ∨ a ≤ c- Defined in
- Mathlib.Order.MinMax
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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_sup_iffproof · cited by 7
Cited by26
Results whose statement or proof uses this declaration.
- IsNonarchimedean.apply_sum_le_supproof · cited by 6
- Polynomial.natDegree_add_leproof · cited by 6
- le_absproof · cited by 5
- IsUltrametricDist.dist_eq_max_of_dist_ne_distproof · cited by 2
- Asymptotics.bound_of_isBigO_cofiniteproof · cited by 2
- IsNonarchimedean.add_eq_max_of_ne'proof · cited by 1
- seminormFromBounded_isNonarchimedeanproof · cited by 1
- Valuation.norm_add_leproof · cited by 1
- Module.Basis.norm_isNonarchimedeanproof · cited by 1
- IsNonarchimedean.multiset_image_add_of_nonemptyproof · cited by 1
- RatFunc.intDegree_add_leproof · cited by 1
- Nat.max_log_padicValNat_succ_eq_log_succproof · cited by 1