Theorems · Theorem · commutative algebra
SModEq.sub_mem
∀ {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 y : M}, x ≡ y [SMOD U] ↔ x - y ∈ U- Defined in
- Mathlib.LinearAlgebra.SModEq.Basic
- Cited by
- 5 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.
Cites7
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
- SModEqstatement · cited by 80
- Submodule.Quotient.eqproof · cited by 21
- SModEq.defproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- SModEq.pow_mul_of_leproof · cited by 1
- Submodule.vadd_set_subset_vadd_set_iffproof · cited by 1
- IsAdicComplete.le_jacobson_botproof · cited by 1
- SModEq.smul'proof · cited by 1