Theorems · Theorem · commutative algebra
Shrink.linearEquiv_apply
∀ (R : Type u_1) (α : Type u_2) [inst : Small.{v, u_2} α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid α]
[inst_3 : Module R α] (a : Shrink.{v, u_2} α), (Shrink.linearEquiv R α) a = (equivShrink α).symm a- Defined in
- Mathlib.Algebra.Module.Shrink
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Equivstatement · cited by 8,337
- Equiv.symmstatement · cited by 3,681
- LinearEquivstatement · cited by 3,317
- Smallstatement and proof · cited by 369
- Shrinkstatement and proof · cited by 132
- equivShrinkstatement · cited by 118
- Shrink.linearEquivstatement and proof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- Module.Baer.of_injectiveproof · cited by 5
- ModuleCat.hasProjectiveDimensionLE_of_semiLinearEquivproof · cited by 3
- ModuleCat.shortExact_projectiveShortComplexproof · cited by 1
- ModuleCat.isSeparatorproof · cited by 0