Theorems · Theorem · order theory
max_le
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α}, a ≤ c → b ≤ c → max a b ≤ c- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 71 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- 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
- max_def'proof · cited by 7
Cited by71
Results whose statement or proof uses this declaration.
- max_commproof · cited by 41
- Cardinal.add_eq_maxproof · cited by 13
- Cardinal.mul_eq_maxproof · cited by 8
- Cardinal.mk_finsupp_lift_of_infiniteproof · cited by 6
- max_assocproof · cited by 5
- eq_maxproof · cited by 4
- Asymptotics.IsBigOWith.prod_left_sameproof · cited by 3
- limsup_maxproof · cited by 3
- Valued.isOpen_closedBallproof · cited by 3
- Polynomial.monic_X_pow_addproof · cited by 3
- PSet.rank_insertproof · cited by 3
- IsUltrametricDist.closedBall_eq_of_memproof · cited by 3