Theorems · Theorem · commutative algebra
Ideal.add_mem_iff_left
∀ {α : Type u} [inst : Ring α] (I : Ideal α) {a b : α}, b ∈ I → (a + b ∈ I ↔ a ∈ I)- Defined in
- Mathlib.RingTheory.Ideal.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Submodule.add_mem_iff_leftproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.inertia_le_stabilizerproof · cited by 1
- Ideal.isPrime_map_C_iff_isPrimeproof · cited by 0