Theorems · Theorem · order theory
not_isMax_of_lt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a < b → ¬IsMax a- Defined in
- Mathlib.Order.Max
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- IsMaxstatement and proof · cited by 372
- IsMax.not_ltproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- LT.lt.not_isMaxproof · cited by 11
- IsMax.isPredPrelimitproof · cited by 5
- strictMonoOn_of_lt_succproof · cited by 4
- Order.lt_succ_iff_not_isMaxproof · cited by 3
- Order.not_isMax_predproof · cited by 0
- SSet.Subcomplex.Pairing.RankFunction.iSup_filtration_iioproof · cited by 0