Theorems · Theorem · group theory
neg_add_eq_iff_eq_add
∀ {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
- 7 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 by7
Results whose statement or proof uses this declaration.
- QuotientAddGroup.leftRel_applyproof · cited by 20
- AddSemiconjBy.neg_symm_left_iffproof · cited by 3
- SimpleGraph.addCayley_adjproof · cited by 2
- Set.vadd_graphOnproof · cited by 1
- AddSubgroup.add_injective_of_disjointproof · cited by 0
- MeasureTheory.pairwise_disjoint_addFundamentalInteriorproof · cited by 0
- add_zsmul_addproof · cited by 0