Theorems · Definition · order theory

OrderMonoidHom.inr

(α : Type u_1) →
  (β : Type u_2) →
    [inst : Monoid α] → [inst_1 : PartialOrder α] → [inst_2 : Monoid β] → [inst_3 : Preorder β] → β →*o α × β

Given ordered monoids M, N, the natural inclusion ordered homomorphism from N to M × N.

Defined in: Mathlib.Algebra.Order.Monoid.Lex
Cited by: 5 results in Mathlib
Foundations: Depth 13 from the axioms · uses propext
Assumes: Monoid PartialOrder Monoid Preorder

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

Cites6

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
PartialOrderstatement and proof · cited by 6,410
Monoidstatement and proof · cited by 3,887
MonoidHomproof · cited by 3,629
OrderMonoidHomstatement · cited by 67
MonoidHom.inrproof · cited by 32

Cited by6

Results whose statement or proof uses this declaration.

OrderMonoidHom.inrₗproof · cited by 5
OrderMonoidHom.inr_applystatement and proof · cited by 1
OrderMonoidHom.fst_comp_inrstatement · cited by 0
OrderMonoidHom.commute_inl_inrstatement · cited by 0
OrderMonoidHom.snd_comp_inrstatement · cited by 0
OrderMonoidHom.inl_mul_inr_eq_mkstatement · cited by 0