Theorems · Theorem · linear algebra

LinearPMap.sup_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] [inst_5 : Module S F] {f g : E →ₛₗ.[σ] F}
  (H : ∀ (x : ↥f.domain) (y : ↥g.domain), ↑x = ↑y → ↑f x = ↑g y) (x : ↥f.domain) (y : ↥g.domain)
  (z : ↥(f.domain ⊔ g.domain)), ↑x + ↑y = ↑z → ↑(f.sup g H) z = ↑f x + ↑g y

Defined in

Mathlib.LinearAlgebra.LinearPMap

Cited by

3 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingAddCommGroupModuleAddCommGroupModule