Theorems · Theorem · linear algebra

LinearPMap.ext

∀ {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 g : E →ₛₗ.[σ] F},
  f.domain = g.domain → (∀ ⦃x : E⦄ ⦃hf : x ∈ f.domain⦄ ⦃hg : x ∈ g.domain⦄, ↑f ⟨x, hf⟩ = ↑g ⟨x, hg⟩) → f = g

Defined in

Mathlib.LinearAlgebra.LinearPMap

Cited by

5 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

RingRingAddCommGroupModuleAddCommGroupModule