Theorems · Theorem · group theory
vadd_left_cancel_iff
∀ {α : Type u_5} {β : Type u_6} [inst : AddGroup α] [inst_1 : AddAction α β] (g : α) {x y : β}, g +ᵥ x = g +ᵥ y ↔ x = y- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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
- AddAction.injectiveproof · cited by 24
Cited by7
Results whose statement or proof uses this declaration.
- AddAction.fixedBy_mem_fixedBy_of_addCommuteproof · cited by 2
- AddAction.vadd_mem_fixedBy_iff_mem_fixedByproof · cited by 2
- SubAddAction.addConjMap_ofFixingAddSubgroup_bijectiveproof · cited by 1
- SubAddAction.exists_vadd_of_last_eqproof · cited by 1
- AddAction.stabilizer_vadd_eq_stabilizer_map_addConjproof · cited by 1
- IsAddUnit.vadd_left_cancelproof · cited by 0
- AddAction.Supports.vaddproof · cited by 0