Theorems · Theorem · group theory
AddSemiconjBy.neg_symm_left_iff
∀ {G : Type u_1} [inst : AddGroup G] {a x y : G}, AddSemiconjBy (-a) y x ↔ AddSemiconjBy a x y- Defined in
- Mathlib.Algebra.Group.Semiconj.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- add_assocproof · cited by 746
- AddSemiconjBystatement · cited by 56
- eq_add_neg_iff_add_eqproof · cited by 12
- neg_add_eq_iff_eq_addproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- AddSemiconjBy.neg_right_iffproof · cited by 3
- AddCommute.neg_left_iffproof · cited by 1
- AddSemiconjBy.neg_symm_leftproof · cited by 0