Theorems · Theorem · order theory
one_lt_iff_ne_one
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : One α] [IsBotOneClass α], 1 < a ↔ a ≠ 1- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- PartialOrderOneIsBotOneClass
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.
- PartialOrderstatement and proof · cited by 6,410
- IsBotOneClassstatement and proof · cited by 35
- LE.le.lt_iff_neproof · cited by 34
- one_leproof · cited by 23
Cited by3
Results whose statement or proof uses this declaration.
- one_lt_of_ne_oneproof · cited by 2
- lt_iff_exists_mulproof · cited by 0
- exists_one_lt_mul_of_ltproof · cited by 0