Theorems · Theorem · group theory
add_mem_cancel_left
∀ {G : Type u_1} [inst : AddGroup G] {S : Type u_4} {H : S} [inst_1 : SetLike S G] [AddSubgroupClass S G] {x y : G},
x ∈ H → (x + y ∈ H ↔ y ∈ H)- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SetLikestatement and proof · cited by 1,084
- AddSubgroupClassstatement and proof · cited by 240
- AddMemClass.add_memproof · cited by 229
- neg_add_cancel_leftproof · cited by 84
- NegMemClass.neg_memproof · cited by 63
Cited by8
Results whose statement or proof uses this declaration.
- Submodule.add_mem_iff_rightproof · cited by 8
- AddSubgroup.index_eq_two_iffproof · cited by 5
- AddSubgroup.add_mem_cancel_leftproof · cited by 4
- vadd_coe_setproof · cited by 3
- AddSubgroup.add_mem_iff_of_index_twoproof · cited by 1
- AddSubgroupClass.subset_unionproof · cited by 1
- leftAddCoset_mem_leftAddCosetproof · cited by 0
- AddAction.IsBlock.of_orbitproof · cited by 0