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Theorems · Theorem · group theory

AddMonoid.Coprod.mk_of_neg_add

∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] (x : G ⊕ H),
  AddMonoid.Coprod.mk (FreeAddMonoid.of (Sum.map Neg.neg Neg.neg x)) + AddMonoid.Coprod.mk (FreeAddMonoid.of x) = 0
Defined in
Mathlib.GroupTheory.Coprod.Basic
Cited by
1 results in Mathlib
Foundations
Depth 48 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddGroup
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Around this declaration

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

AddMonoid.Coprod.con_neg_add_cancel · cited by 0Coprod.con_neg_add_cancelDFunLike.coe · cited by 62936DFunLike.coeAddGroup · cited by 4410AddGroupAddMonoidHom · cited by 3230AddMonoidHomneg_add_cancel · cited by 256neg_add_cancelFreeAddMonoid · cited by 145FreeAddMonoidAddMonoid.Coprod · cited by 104AddMonoid.CoprodFreeAddMonoid.of · cited by 69FreeAddMonoid.ofAddMonoid.Coprod.inl · cited by 42Coprod.inlAddMonoid.Coprod.inr · cited by 42Coprod.inrAddMonoid.Coprod.mk · cited by 16Coprod.mkmap_add_eq_zero · cited by 5map_add_eq_zeroCoprod.mk_of_neg_addCITED BYCITES

Cites11

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Cited by1

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