Theorems · Theorem · group theory
eq_neg_add_iff_add_eq
∀ {G : Type u_3} [inst : AddGroup G] {a b c : G}, a = -b + c ↔ b + a = c- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- neg_add_cancel_leftproof · cited by 84
- add_neg_cancel_leftproof · cited by 76
Cited by16
Results whose statement or proof uses this declaration.
- Int.cast_addproof · cited by 124
- QuotientAddGroup.rightRel_applyproof · cited by 6
- AddSubgroup.mem_normalizer_iff_addConj_image_eqproof · cited by 3
- max_neg_zeroproof · cited by 3
- vadd_ball''proof · cited by 2
- SimpleGraph.addCayley_adjproof · cited by 2
- QuotientAddGroup.leftRel_eq_topproof · cited by 1
- Set.vadd_graphOnproof · cited by 1
- RootPairing.chainBotCoeff_mul_chainTopCoeff.isNotG2proof · cited by 1
- QuotientAddGroup.mk'_eq_mk'proof · cited by 1
- Set.neg_mem_addCentralizerproof · cited by 1
- AddGroupExtension.Section.exists_add_eq_add_add_inlproof · cited by 0