Theorems · Theorem · group theory
add_neg_eq_iff_eq_add
∀ {G : Type u_3} [inst : AddGroup G] {a b c : G}, a + -b = c ↔ a = c + b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 12 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_rightproof · cited by 75
- add_neg_cancel_rightproof · cited by 65
Cited by12
Results whose statement or proof uses this declaration.
- sub_eq_iff_eq_addproof · cited by 74
- posPart_sub_negPartproof · cited by 9
- QuotientAddGroup.rightRel_applyproof · cited by 6
- AddSubgroup.upperCentralSeries_oneproof · cited by 4
- AddSubgroup.mem_normalizer_iff_addConj_image_eqproof · cited by 3
- isAddConj_iffproof · cited by 3
- addCommutatorElement_eq_zero_iff_add_commproof · cited by 3
- AddSubgroup.mem_centralizer_iff_addCommutator_eq_zeroproof · cited by 1
- Set.neg_mem_addCentralizerproof · cited by 1
- AddSubgroup.mem_centralizer_iff_addCommutator_eq_zero'proof · cited by 0
- mem_addCommutatorSet_of_isAddConj_sqproof · cited by 0
- CategoryTheory.isCommAddMonObj_iff_addCommutator_eq_toAddUnit_ηproof · cited by 0