Theorems · Theorem · order theory
not_supPrime
∀ {α : Type u_2} [inst : SemilatticeSup α] {a : α}, ¬SupPrime a ↔ IsMin a ∨ ∃ b c, a ≤ b ⊔ c ∧ ¬a ≤ b ∧ ¬a ≤ c- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 1 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
- SupPrimestatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- not_infPrimeproof · cited by 0