Theorems · Theorem · commutative algebra
Module.Dual.exists_forall_ne_zero_of_forall_exists
∀ {ι : Type u_1} {K : Type u_2} {M : Type u_3} [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M]
[Finite ι] [Infinite K] (f : ι → Module.Dual K M), (∀ (i : ι), ∃ x, (f i) x ≠ 0) → ∃ x, ∀ (i : ι), (f i) x ≠ 0- Defined in
- Mathlib.Algebra.Module.Submodule.Union
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- Finitestatement and proof · cited by 3,029
- LinearMap.kerproof · cited by 848
- Module.Dualstatement and proof · cited by 583
- Infinitestatement and proof · cited by 352
- Submodule.exists_forall_notMem_of_forall_ne_topproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Module.Dual.exists_forall_mem_ne_zero_of_forall_existsproof · cited by 1
- Module.exists_dual_forall_apply_ne_zeroproof · cited by 1