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Theorems · Theorem · order theory

OrderIso.injective

∀ {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] (e : α ≃o β), Function.Injective ⇑e
Defined in
Mathlib.Order.Hom.Basic
Cited by
28 results in Mathlib
Foundations
Depth 22 from the axioms · uses Quot.sound
Assumes
LELE
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Around this declaration

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

NumberField.absNorm_differentIdeal · cited by 4NumberField.absNorm_diffe…AddSubmonoid.op_injective · cited by 2AddSubmonoid.op_injectiveSubring.op_injective · cited by 2Subring.op_injectiveSubsemigroup.unop_injective · cited by 2Subsemigroup.unop_injecti…Subgroup.unop_injective · cited by 2Subgroup.unop_injectiveAddSubgroup.unop_injective · cited by 2AddSubgroup.unop_injectiveSubsemiring.unop_injective · cited by 2Subsemiring.unop_injectiveSubsemigroup.op_injective · cited by 2Subsemigroup.op_injectiveSubring.unop_injective · cited by 2Subring.unop_injectiveSubmonoid.op_injective · cited by 2Submonoid.op_injectiveSubgroup.op_injective · cited by 2Subgroup.op_injectiveAddSubsemigroup.unop_injective · cited by 2AddSubsemigroup.unop_inje…Subsemiring.op_injective · cited by 2Subsemiring.op_injectiveAddSubgroup.op_injective · cited by 2AddSubgroup.op_injectiveAddSubmonoid.unop_injective · cited by 2AddSubmonoid.unop_injecti…DFunLike.coe · cited by 62936DFunLike.coeOrderIso · cited by 874OrderIsoEquiv.injective · cited by 464Equiv.injectiveRelIso.toEquiv · cited by 113RelIso.toEquivOrderIso.injectiveCITED BYCITES

Cites4

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

Cited by28

Results whose statement or proof uses this declaration.