Theorems · Definition · order theory

OrderAddMonoidHom.inl

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

Given ordered additive monoids M, N, the natural inclusion ordered homomorphism from M 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: AddMonoid PartialOrder AddMonoid 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
AddMonoidHomproof · cited by 3,230
AddMonoidstatement and proof · cited by 2,864
OrderAddMonoidHomstatement · cited by 80
AddMonoidHom.inlproof · cited by 29

Cited by6

Results whose statement or proof uses this declaration.

OrderAddMonoidHom.inlₗproof · cited by 4
OrderAddMonoidHom.inl_applystatement and proof · cited by 1
OrderAddMonoidHom.fst_comp_inlstatement · cited by 0
OrderAddMonoidHom.snd_comp_inlstatement · cited by 0
OrderAddMonoidHom.addCommute_inl_inrstatement · cited by 0
OrderAddMonoidHom.inl_add_inr_eq_mkstatement · cited by 0