Theorems · Theorem · group theory
AddSubmonoid.closure_sdiff_eq_closure
∀ {M : Type u_1} [inst : AddZeroClass M] {s t : Set M},
t ⊆ ↑(AddSubmonoid.closure (s \ t)) → AddSubmonoid.closure (s \ t) = AddSubmonoid.closure s- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 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.
Cites12
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.coestatement and proof · cited by 8,199
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- LE.le.antisymmproof · cited by 507
- SetLike.mem_coeproof · cited by 302
- AddSubmonoid.closurestatement and proof · cited by 224
- Set.sdiff_subsetproof · cited by 156
- AddSubmonoid.closure_leproof · cited by 35
- AddSubmonoid.closure_monoproof · cited by 10
- AddSubmonoid.mem_closureproof · cited by 8
- Set.mem_sdiff_of_memproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.closure_sdiff_singleton_zeroproof · cited by 1
- AddSubmonoid.closure_addIrreducibleproof · cited by 0