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Theorems · Theorem · order theory

Ne.one_lt

∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : One α] [IsBotOneClass α], a ≠ 1 → 1 < a

Alias of one_lt_of_ne_one. Alias of the reverse direction of one_lt_iff_ne_one.

Defined in
Mathlib.Algebra.Order.IsBotOne
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
PartialOrderOneIsBotOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NE.ne.one_lt · cited by 0ne.one_ltPartialOrder · cited by 6410PartialOrderIsBotOneClass · cited by 35IsBotOneClassone_lt_of_ne_one · cited by 2one_lt_of_ne_oneNe.one_ltCITED BYCITES

Cites3

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Cited by1

Results whose statement or proof uses this declaration.