Theorems · Theorem · functional analysis
Submodule.prodEquivOfIsTopCompl_apply
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : TopologicalSpace M] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] {p q : Submodule R M} [inst_4 : IsTopologicalAddGroup M] (h : Submodule.IsTopCompl p q)
(x : ↥p × ↥q), (p.prodEquivOfIsTopCompl q h) x = ↑x.1 + ↑x.2- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- ContinuousLinearEquivstatement · cited by 743
- Submodule.IsTopComplstatement and proof · cited by 89
- Submodule.prodEquivOfIsTopComplstatement · cited by 6
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