Theorems · Theorem · linear algebra

LinearPMap.coprod_apply

∀ {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] {G : Type u_6} [inst_5 : AddCommGroup G]
  [inst_6 : Module R F] [inst_7 : Module S G] (f : E →ₛₗ.[σ] G) (g : F →ₛₗ.[σ] G) (x : ↥(f.coprod g).domain),
  ↑(f.coprod g) x = ↑f ⟨(↑x).1, ⋯⟩ + ↑g ⟨(↑x).2, ⋯⟩

Defined in

Mathlib.LinearAlgebra.LinearPMap

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

RingRingAddCommGroupModuleAddCommGroupAddCommGroupModuleModule