Theorems · Theorem · linear algebra
LinearPMap.mem_graph_iff
∀ {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 : E →ₗ.[R] F) {x : E × F}, x ∈ f.graph ↔ ∃ y, ↑y = x.1 ∧ ↑f y = x.2- Defined in
- Mathlib.LinearAlgebra.LinearPMap
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, 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.
- 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.domainstatement and proof · cited by 167
- LinearPMap.toFun'statement and proof · cited by 124
- LinearPMap.graphstatement · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.toLinearPMap_graph_eqproof · cited by 4
- LinearPMap.le_graph_of_leproof · cited by 3
- LinearPMap.smul_graphproof · cited by 0
- LinearPMap.neg_graphproof · cited by 0