Theorems · Theorem · commutative algebra
Module.Projective.out
∀ {R : Type u_1} {inst : Semiring R} {P : Type u_2} {inst_1 : AddCommMonoid P} {inst_2 : Module R P}
[self : Module.Projective R P], ∃ s, Function.LeftInverse ⇑(Finsupp.linearCombination R id) ⇑s- Defined in
- Mathlib.Algebra.Module.Projective
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Module.Projective
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.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Finsuppstatement · cited by 5,255
- Finsupp.linearCombinationstatement · cited by 269
- Module.Projectivestatement and proof · cited by 82
Cited by2
Results whose statement or proof uses this declaration.
- Module.projective_lifting_propertyproof · cited by 13
- Module.projective_defproof · cited by 0