Theorems · Theorem · field theory
UniformSpace.Completion.mul_hatInv_cancel
∀ {K : Type u_1} [inst : Field K] [inst_1 : UniformSpace K] [IsTopologicalDivisionRing K] [CompletableTopField K]
[IsUniformAddGroup K] {x : UniformSpace.Completion K}, x ≠ 0 → x * x.hatInv = 1- Defined in
- Mathlib.Topology.Algebra.UniformField
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Set.imageproof · cited by 5,609
- nhdsproof · cited by 5,554
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- Compl.complproof · cited by 2,925
- UniformSpacestatement and proof · cited by 2,040
- closureproof · cited by 1,254
- ContinuousAtproof · cited by 697
- IsUniformAddGroupstatement and proof · cited by 342
- Set.image_univproof · cited by 322
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.