Theorems · Definition · order theory

OrderMonoidIso.unitsCongr

{α : Type u_1} →
  {β : Type u_2} →
    [inst : Preorder α] → [inst_1 : Monoid α] → [inst_2 : Preorder β] → [inst_3 : Monoid β] → (α ≃*o β) → αˣ ≃*o βˣ

An isomorphism of ordered monoids descends to their units.

Defined in: Mathlib.Algebra.Order.Hom.Units
Cited by: 5 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Quot.sound
Assumes: Preorder Monoid Preorder Monoid

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Around this declaration

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

Cites7

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

Preorderstatement and proof · cited by 7,952
Monoidstatement and proof · cited by 3,887
Unitsstatement and proof · cited by 2,804
MulEquivproof · cited by 1,142
OrderMonoidIsostatement and proof · cited by 114
OrderMonoidIso.toMulEquivproof · cited by 20
Units.mapEquivproof · cited by 16

Cited by5

Results whose statement or proof uses this declaration.

OrderMonoidIso.unitsCongr_symm_applystatement · cited by 0
OrderMonoidIso.val_inv_unitsCongr_applystatement and proof · cited by 0
OrderMonoidIso.val_inv_unitsCongr_symm_applystatement and proof · cited by 0
OrderMonoidIso.val_unitsCongr_applystatement and proof · cited by 0
OrderMonoidIso.val_unitsCongr_symm_applystatement and proof · cited by 0