Theorems · Theorem · commutative algebra
UniformSpace.Completion.coe_mul
∀ {α : Type u_1} [inst : Ring α] [inst_1 : UniformSpace α] [IsTopologicalRing α] (a b : α), ↑(a * b) = ↑a * ↑b- Defined in
- Mathlib.Topology.Algebra.UniformRing
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- UniformSpacestatement and proof · cited by 2,040
- IsTopologicalRingstatement and proof · cited by 402
- Continuous.compproof · cited by 371
- UniformSpace.Completionstatement · cited by 192
- UniformSpace.Completion.coe'statement · cited by 144
- continuous_mulproof · cited by 41
- UniformSpace.Completion.isDenseInducing_coeproof · cited by 11
- IsDenseInducing.extend_eqproof · cited by 9
- UniformSpace.Completion.continuous_coeproof · cited by 8
- IsDenseInducing.prodMapproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.coeRingHomproof · cited by 3
- HasSum.mul_of_nonarchimedeanproof · cited by 2
- Valued.continuous_extensionproof · cited by 2
- NumberField.InfinitePlace.Completion.coe_mulproof · cited by 0
- UniformSpace.Completion.mul_hatInv_cancelproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.adicCompletion.coe_mulproof · cited by 0
- UniformSpace.Completion.map_smul_eq_mul_coeproof · cited by 0