Theorems · Theorem · linear algebra
LinearPMap.le_of_le_graph
∀ {R : Type u_1} [inst : Ring R] {E : Type u_4} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {F : Type u_5}
[inst_3 : AddCommGroup F] [inst_4 : Module R F] {f g : E →ₗ.[R] F}, f.graph ≤ g.graph → f ≤ g- Defined in
- Mathlib.LinearAlgebra.LinearPMap
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- LinearPMapstatement and proof · cited by 179
- LinearPMap.domainproof · cited by 167
- LinearPMap.toFun'proof · cited by 124
- LinearPMap.graphstatement and proof · cited by 39
- LinearPMap.mem_domain_iffproof · cited by 2
- LinearPMap.image_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- LinearPMap.eq_of_eq_graphproof · cited by 3
- LinearPMap.le_closureproof · cited by 2
- LinearPMap.le_graph_iffproof · cited by 0
- LinearPMap.IsClosable.closure_monoproof · cited by 0