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Theorems · Theorem · order theory

LT.lt.one_lt

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

Alias of one_lt_of_gt.

Defined in
Mathlib.Algebra.Order.IsBotOne
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
PreorderOneIsBotOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ne_one_of_lt · cited by 1ne_one_of_ltPNat.one_lt_of_lt · cited by 0PNat.one_lt_of_ltPreorder · cited by 7952PreorderIsBotOneClass · cited by 35IsBotOneClassone_lt_of_gt · cited by 1one_lt_of_gtlt.one_ltCITED 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.