Mathlib Map

Theorems · Theorem · order theory

SupPrime.le_sup

∀ {α : Type u_2} [inst : SemilatticeSup α] {a b c : α}, SupPrime a → (a ≤ b ⊔ c ↔ a ≤ b ∨ a ≤ c)
Defined in
Mathlib.Order.Irreducible
Cited by
1 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
SemilatticeSup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SupPrime.le_finset_sup · cited by 1SupPrime.le_finset_supSemilatticeSup · cited by 785SemilatticeSuple_sup_of_le_left · cited by 26le_sup_of_le_leftSupPrime · cited by 19SupPrimele_sup_of_le_right · cited by 17le_sup_of_le_rightSupPrime.le_supCITED BYCITES

Cites4

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

Cited by1

Results whose statement or proof uses this declaration.