Theorems · Theorem · linear algebra
Submodule.mulMap_range
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] (M N : Submodule R S),
(M.mulMap N).range = M * N- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement and proof · cited by 2,545
- le_antisymmproof · cited by 2,068
- map_zeroproof · cited by 1,614
- TensorProduct.tmulproof · cited by 1,182
- map_addproof · cited by 964
- LinearMap.rangestatement and proof · cited by 893
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.mulMap'proof · cited by 2
- Submodule.LinearDisjoint.mulMapproof · cited by 2
- Module.Flat.top_mul_submoduleAlgebraproof · cited by 1
- Submodule.mulMap'_surjectiveproof · cited by 0