Theorems · Theorem · commutative algebra
AddSubmonoid.one_eq_closure
∀ {R : Type u_2} [inst : AddMonoidWithOne R], 1 = AddSubmonoid.closure {1}- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- AddMonoidHomproof · cited by 3,230
- FunLikeproof · cited by 2,560
- Nat.cast_oneproof · cited by 2,501
- AddZeroClassproof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoidWithOnestatement and proof · cited by 313
- AddMonoidHomClassproof · cited by 252
- AddSubmonoid.closurestatement · cited by 224
- AddMonoidHom.mrangeproof · cited by 61
- nsmul_oneproof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.one_eq_closure_one_setproof · cited by 0