Theorems · Theorem · group theory
AddSemiconjBy.vadd_left_iff
∀ {G : Type u_3} {H : Type u_4} [inst : AddGroup G] [inst_1 : Add H] [inst_2 : AddAction G H] [VAddCommClass G H H]
[VAddAssocClass G H H] {a b x : H} {r : G}, AddSemiconjBy (r +ᵥ x) a b ↔ AddSemiconjBy x a b- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- VAddAssocClassstatement and proof · cited by 60
- AddSemiconjBystatement and proof · cited by 56
- VAddCommClassstatement and proof · cited by 41
- neg_vadd_vaddproof · cited by 34
- AddSemiconjBy.vadd_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddCommute.vadd_left_iffproof · cited by 0