Theorems · Theorem · commutative algebra
IsAddLeftRegular.of_add
∀ {R : Type u_1} [inst : AddSemigroup R] {a b : R}, IsAddLeftRegular (a + b) → IsAddLeftRegular bIf an element b becomes add-left-regular after adding to it on the left
an add-left-regular element, then b is add-left-regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
- Assumes
- AddSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSemigroupstatement and proof · cited by 136
- Function.Injective.of_compproof · cited by 82
- IsAddLeftRegularstatement and proof · cited by 58
- comp_add_leftproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- isAddRegular_add_and_add_iffproof · cited by 2
- isAddLeftRegular_of_add_eq_zeroproof · cited by 2
- IsAddLeftRegular.nsmul_iffproof · cited by 1
- add_isAddLeftRegular_iffproof · cited by 0