Theorems · Theorem · order theory
le_sup_iff
∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a ≤ max b c ↔ a ≤ b ∨ a ≤ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 15 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.
Cites1
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
Cited by7
Results whose statement or proof uses this declaration.
- le_max_iffproof · cited by 26
- IsUltrametricDist.norm_add_le_maxproof · cited by 7
- abs_le_max_abs_absproof · cited by 5
- Finset.le_sup_iffproof · cited by 4
- IsUltrametricDist.isUltrametricDist_of_forall_norm_add_le_max_normproof · cited by 3
- max_eq_topproof · cited by 0
- le_max_of_two_nsmul_le_addproof · cited by 0