Theorems · Theorem · general topology
UniformSpace.Completion.induction_on
∀ {α : Type u_1} [inst : UniformSpace α] {p : UniformSpace.Completion α → Prop} (a : UniformSpace.Completion α),
IsClosed {a | p a} → (∀ (a : α), p ↑a) → p a- Defined in
- Mathlib.Topology.UniformSpace.Completion
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- UniformSpacestatement and proof · cited by 2,040
- IsClosedstatement and proof · cited by 1,639
- UniformSpace.Completionstatement and proof · cited by 192
- UniformSpace.Completion.coe'statement and proof · cited by 144
- isClosed_propertyproof · cited by 13
- UniformSpace.Completion.denseRange_coeproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.Completion.induction_onproof · cited by 3
- Valued.valuedCompletion_surjective_iffproof · cited by 2
- UniformSpace.Completion.dist_selfproof · cited by 1
- Padic.withValUniformEquiv_norm_le_one_iffproof · cited by 0
- AddMonoidHom.completion_addproof · cited by 0
- AddMonoidHom.completion_zeroproof · cited by 0
- UniformSpace.Completion.map_smul_eq_mul_coeproof · cited by 0
- Valuation.IsEquiv.valuedCompletion_le_one_iffproof · cited by 0