Theorems · Theorem · commutative algebra
SModEq.zero
∀ {R : Type u_1} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {U : Submodule R M}
{x : M}, x ≡ 0 [SMOD U] ↔ x ∈ U- Defined in
- Mathlib.LinearAlgebra.SModEq.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- sub_zeroproof · cited by 938
- SModEqstatement · cited by 80
- Submodule.Quotient.eqproof · cited by 21
- SModEq.defproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- PowerSeries.IsWeierstrassDivisorAt.eq_zero_of_mul_eqproof · cited by 1
- IsHausdorff.iInf_pow_smulproof · cited by 0