Mathlib Map

Theorems · Definition · group theory

AddMonoid.Coprod.fst

{M : Type u_1} → {N : Type u_2} → [inst : AddMonoid M] → [inst_1 : AddMonoid N] → AddMonoid.Coprod M N →+ M

The natural projection AddMonoid.Coprod M N →+ M.

Defined in
Mathlib.GroupTheory.Coprod.Basic
Cited by
15 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidAddMonoid
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Around this declaration

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

AddMonoid.Coprod.fst_prod_snd · cited by 3Coprod.fst_prod_sndAddEquiv.coprodPUnit · cited by 2AddEquiv.coprodPUnitAddMonoid.Coprod.fst_apply_inl · cited by 2Coprod.fst_apply_inlAddMonoid.Coprod.fst_comp_toProd · cited by 1Coprod.fst_comp_toProdAddMonoid.Coprod.snd_comp_toProd · cited by 1Coprod.snd_comp_toProdAddEquiv.coprodPUnit_apply · cited by 0AddEquiv.coprodPUnit_applyAddMonoid.Coprod.prod_mk_fst_snd · cited by 0Coprod.prod_mk_fst_sndAddMonoid.Coprod.fst_apply_inr · cited by 0Coprod.fst_apply_inrAddMonoid.Coprod.fst_comp_inl · cited by 0Coprod.fst_comp_inlAddMonoid.Coprod.fst_comp_inr · cited by 0Coprod.fst_comp_inrAddMonoid.Coprod.fst_comp_swap · cited by 0Coprod.fst_comp_swapAddMonoid.Coprod.fst_surjective · cited by 0Coprod.fst_surjectiveAddMonoid.Coprod.fst_swap · cited by 0Coprod.fst_swapAddMonoid.Coprod.fst_toProd · cited by 0Coprod.fst_toProdAddMonoid.Coprod.snd_comp_swap · cited by 0Coprod.snd_comp_swapAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidAddMonoidHom.id · cited by 107AddMonoidHom.idAddMonoid.Coprod · cited by 104AddMonoid.CoprodAddMonoid.Coprod.lift · cited by 13Coprod.liftCoprod.fstCITED BYCITES

Cites5

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

Cited by16

Results whose statement or proof uses this declaration.