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Theorems · Definition · order theory

OrderMonoidHom.fst

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

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

Defined in
Mathlib.Algebra.Order.Monoid.Lex
Cited by
3 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
MonoidPartialOrderMonoidPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderMonoidHom.fst_apply · cited by 0OrderMonoidHom.fst_applyOrderMonoidHom.fst_comp_inl · cited by 0OrderMonoidHom.fst_comp_i…OrderMonoidHom.fst_comp_inr · cited by 0OrderMonoidHom.fst_comp_i…Preorder · cited by 7952PreorderPartialOrder · cited by 6410PartialOrderMonoid · cited by 3887MonoidMonoidHom · cited by 3629MonoidHomOrderMonoidHom · cited by 67OrderMonoidHomMonoidHom.fst · cited by 28MonoidHom.fstOrderMonoidHom.fstCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.