Theorems · Theorem · ring theory
Module.ulift_injective_of_injective
∀ (R : Type u) [inst : Ring R] {M : Type v} [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Small.{v, u} R],
Module.Injective R M → Module.Injective R (ULift.{v', v} M)- Defined in
- Mathlib.Algebra.Module.Injective
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModuleSmall
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Idealproof · cited by 4,748
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- Smallstatement and proof · cited by 369
- Module.Injectivestatement and proof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- Module.injective_iff_ulift_injectiveproof · cited by 0