Theorems · Theorem · linear algebra
Submodule.inf_sup_assoc_of_le_of_neg_le
∀ {R : Type u_8} {M : Type u_9} [inst : Semiring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {s : Submodule R M}
(t : Submodule R M) {p : Submodule R M}, p ≤ s → -p ≤ s → s ⊓ t ⊔ p = s ⊓ (t ⊔ p)- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- sup_commproof · cited by 165
- inf_commproof · cited by 139
- Submodule.pointwiseNegstatement · cited by 20
- Submodule.sup_inf_assoc_of_le_of_neg_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- PointedCone.inf_sup_assoc_of_le_of_submodule_leproof · cited by 0