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Theorems · Theorem · field theory

Valued.closure_coe_completion_v_lt

∀ {K : Type u_1} [inst : Field K] {Γ₀ : Type u_2} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [hv : Valued K Γ₀]
  {γ : Γ₀ˣ}, closure (UniformSpace.Completion.coe' '' {x | Valued.v x < ↑γ}) = {x | Valued.extensionValuation x < ↑γ}
Defined in
Mathlib.Topology.Algebra.Valued.ValuedField
Cited by
1 results in Mathlib
Foundations
Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderedCommGroupWithZeroValued

Around this declaration

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Cites42

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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  • Set.extproof · cited by 2,266
  • Units.valstatement and proof · cited by 1,966

Cited by1

Results whose statement or proof uses this declaration.