Theorems · Theorem · group theory
AddSubmonoid.op_closure
∀ {M : Type u_2} [inst : AddZeroClass M] (s : Set M),
(AddSubmonoid.closure s).op = AddSubmonoid.closure (AddOpposite.unop ⁻¹' s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.preimagestatement and proof · cited by 4,946
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- InfSet.sInfproof · cited by 935
- AddOppositestatement and proof · cited by 452
- AddSubmonoid.closurestatement · cited by 224
- Function.Surjective.forallproof · cited by 214
- AddOpposite.opproof · cited by 192
- InfSetproof · cited by 145
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.closure_induction_rightproof · cited by 1
- AddSubmonoid.unop_closureproof · cited by 0