Theorems · Theorem · order theory
IsMax.eq_of_ge
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, IsMax a → a ≤ b → b = a- Defined in
- Mathlib.Order.Max
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- IsMaxstatement and proof · cited by 372
- LE.le.antisymm'proof · cited by 104
Cited by7
Results whose statement or proof uses this declaration.
- Order.succ_eq_iff_isMaxproof · cited by 11
- IsMax.Ici_eqproof · cited by 3
- csInf_mem_of_not_isPredLimitproof · cited by 3
- PrimeSpectrum.isOpen_singleton_tfae_of_isNoetherian_of_isJacobsonRingproof · cited by 2
- Module.Baer.extensionOfMax_is_maxproof · cited by 1
- IsCofinal.mem_of_isMaxproof · cited by 1
- IsBot.not_isMaxproof · cited by 1