Theorems · Theorem · ring theory
Ideal.closure_eq_of_isClosed
∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : Ring R] [inst_2 : IsTopologicalRing R] (I : Ideal R),
IsClosed ↑I → I.closure = IThis is not @[simp] since otherwise it causes timeouts downstream as simp tries and fails to
generate an IsClosed instance.
https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.234852.20heartbeats.20of.20the.20linter
- Defined in
- Mathlib.Topology.Algebra.Ring.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- IsClosedstatement and proof · cited by 1,639
- IsTopologicalRingstatement and proof · cited by 402
- IsClosed.closure_eqproof · cited by 139
- SetLike.ext'proof · cited by 60
- Ideal.closurestatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.ideal_isMaximal_iffproof · cited by 1