Theorems · Theorem · group theory
vadd_eq_iff_eq_neg_vadd
∀ {α : Type u_5} {β : Type u_6} [inst : AddGroup α] [inst_1 : AddAction α β] (g : α) {x y : β}, g +ᵥ x = y ↔ x = -g +ᵥ y- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 1,820
- AddActionstatement and proof · cited by 820
- eq_neg_vadd_iffproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- isCancelVAdd_iff_eq_zero_of_vadd_eqproof · cited by 2
- AddAction.IsBlock.of_subsetproof · cited by 1
- AddAction.period_negproof · cited by 0
- Finset.vadd_finset_eq_univproof · cited by 0
- Set.vadd_set_eq_univproof · cited by 0
- AddAction.vadd_fixedByproof · cited by 0