Theorems · Theorem · linear algebra
Submodule.Quotient.mk_out
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {p : Submodule R M}
(m : M ⧸ p), Submodule.Quotient.mk (Quotient.out m) = m- Defined in
- Mathlib.LinearAlgebra.Quotient.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites9
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 and proof · cited by 2,301
- Submodule.Quotient.mkstatement · cited by 184
- Quotient.outstatement · cited by 141
- Quotient.out_eqproof · cited by 27
- Submodule.quotientRelstatement · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_le_ker_evalproof · cited by 1