Theorems · Theorem · linear algebra
LinearPMap.map_sub
∀ {R : Type u_1} {S : Type u_2} [inst : Ring R] [inst_1 : Ring S] {σ : R →+* S} {E : Type u_4} [inst_2 : AddCommGroup E]
[inst_3 : Module R E] {F : Type u_5} [inst_4 : AddCommGroup F] [inst_5 : Module S F] (f : E →ₛₗ.[σ] F)
(x y : ↥f.domain), ↑f (x - y) = ↑f x - ↑f y- Defined in
- Mathlib.LinearAlgebra.LinearPMap
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AddCommGroupstatement and proof · cited by 12,871
- RingHomstatement and proof · cited by 10,189
- 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 · cited by 124
- LinearPMap.toFunproof · cited by 34
- LinearMap.map_subproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- HahnEmbedding.Partial.coeff_eq_of_memproof · cited by 2
- HahnEmbedding.Partial.eval_ltproof · cited by 1
- HahnEmbedding.Seed.baseEmbedding_strictMonoproof · cited by 1
- HahnEmbedding.Partial.archimedeanClassMk_le_of_eval_eqproof · cited by 1
- HahnEmbedding.Partial.sSupFun_strictMonoproof · cited by 1
- RieszExtension.stepproof · cited by 1
- HahnEmbedding.Partial.extendFun_strictMonoproof · cited by 1