Theorems · Theorem · group theory
AddSubmonoid.closure_eq_of_le
∀ {M : Type u_1} [inst : AddZeroClass M] {s : Set M} {S : AddSubmonoid M},
s ⊆ ↑S → S ≤ AddSubmonoid.closure s → AddSubmonoid.closure s = S- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 3 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.
Cites7
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
- le_antisymmproof · cited by 2,068
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- AddSubmonoid.closure_leproof · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.span_nat_eq_addSubmonoidClosureproof · cited by 5
- AddSubmonoid.closure_singleton_eqproof · cited by 2
- AddSubmonoid.closure_isSquareproof · cited by 0