Theorems · Theorem · linear algebra
Submodule.map.congr_simp
∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}
[inst_6 : RingHomSurjective σ₁₂] (f f_1 : M →ₛₗ[σ₁₂] M₂),
f = f_1 → ∀ (p p_1 : Submodule R M), p = p_1 → Submodule.map f p = Submodule.map f_1 p_1- Defined in
- Mathlib.Algebra.Module.Submodule.Map
- Cited by
- 75 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- Submodule.mapstatement and proof · cited by 614
- RingHomSurjectivestatement and proof · cited by 220
Cited by75
Results whose statement or proof uses this declaration.
- AffineSubspace.map_spanproof · cited by 16
- Module.Basis.ofZLatticeBasis_spanproof · cited by 6
- Submodule.range_projectionproof · cited by 6
- AddMonoidAlgebra.supported_eq_span_singleproof · cited by 5
- AffineSubspace.Parallel.direction_eqproof · cited by 4
- Submodule.exists_dual_map_eq_bot_of_notMemproof · cited by 4
- Module.End.independent_genEigenspaceproof · cited by 4
- Module.FinitePresentation.exists_finproof · cited by 4
- LieAlgebra.mem_corootSpaceproof · cited by 4
- Submodule.lift_spanRank_map_leproof · cited by 3
- EuclideanGeometry.orthogonalProjection_mapproof · cited by 3
- Module.finitePresentation_of_free_of_surjectiveproof · cited by 3