Theorems · Theorem · commutative algebra
SModEq.def
∀ {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] ↔ Submodule.Quotient.mk x = Submodule.Quotient.mk y- Defined in
- Mathlib.LinearAlgebra.SModEq.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 71 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
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.Quotient.mkstatement · cited by 184
- SModEqstatement · cited by 80
Cited by9
Results whose statement or proof uses this declaration.
- SModEq.sub_memproof · cited by 5
- SModEq.zeroproof · cited by 3
- SModEq.addproof · cited by 2
- AdicCompletion.mk_surjectiveproof · cited by 1
- SModEq.botproof · cited by 0
- SModEq.zsmulproof · cited by 0
- SModEq.nsmulproof · cited by 0
- SModEq.smulproof · cited by 0
- SModEq.subproof · cited by 0