Theorems · Theorem · order theory
not_supIrred
∀ {α : Type u_2} [inst : SemilatticeSup α] {a : α}, ¬SupIrred a ↔ IsMin a ∨ ∃ b c, b ⊔ c = a ∧ b < a ∧ c < a- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeSupstatement and proof · cited by 785
- IsMinstatement and proof · cited by 277
- not_and_orproof · cited by 82
- SupIrredstatement · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- exists_supIrred_decompositionproof · cited by 1
- not_infIrredproof · cited by 0