Theorems · Theorem · functional analysis
ClosedSubmodule.ext
∀ {R : Type u_2} {M : Type u_3} {inst : Semiring R} {inst_1 : AddCommMonoid M} {inst_2 : TopologicalSpace M}
{inst_3 : Module R M} {x y : ClosedSubmodule R M}, (↑x).carrier = (↑y).carrier → x = y- Cited by
- 15 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- IsClosedproof · cited by 1,639
- AddSubmonoid.toAddSubsemigroupstatement and proof · cited by 198
- AddSubsemigroup.carrierstatement and proof · cited by 198
- Submodule.toAddSubmonoidstatement and proof · cited by 162
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement and proof · cited by 51
Cited by15
Results whose statement or proof uses this declaration.
- ClosedSubmodule.orthogonal_orthogonal_eqproof · cited by 3
- Submodule.closure_eqproof · cited by 2
- ClosedSubmodule.mulI_mulI_eqproof · cited by 2
- ClosedSubmodule.mulI_orthogonal_eq_symplCompproof · cited by 2
- ClosedSubmodule.mapEquiv_sup_eqproof · cited by 1
- ClosedSubmodule.orthogonal_closure'proof · cited by 1
- ClosedSubmodule.bot_orthogonal_eq_topproof · cited by 1
- ClosedSubmodule.mapEquiv_inf_eqproof · cited by 1
- Submodule.closure_eq'proof · cited by 1
- ClosedSubmodule.mapEquiv_top_eq_topproof · cited by 0
- ClosedSubmodule.top_orthogonal_eq_botproof · cited by 0
- ClosedSubmodule.closure_map_eq_mapEquiv_closureproof · cited by 0