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Theorems · Theorem · order theory

one_lt_of_ne_one

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

Alias of the reverse direction of one_lt_iff_ne_one.

Defined in
Mathlib.Algebra.Order.IsBotOne
Cited by
2 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
PartialOrderOneIsBotOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Submonoid.fg_of_divisive · cited by 2Submonoid.fg_of_divisiveNe.one_lt · cited by 1Ne.one_ltPartialOrder · cited by 6410PartialOrderIsBotOneClass · cited by 35IsBotOneClassone_lt_iff_ne_one · cited by 3one_lt_iff_ne_oneone_lt_of_ne_oneCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.