Theorems · Theorem · geometry

AffineMap.ext

∀ {k : Type u_1} {V1 : Type u_2} {P1 : Type u_3} {V2 : Type u_4} {P2 : Type u_5} [inst : Ring k]
  [inst_1 : AddCommGroup V1] [inst_2 : Module k V1] [inst_3 : AddTorsor V1 P1] [inst_4 : AddCommGroup V2]
  [inst_5 : Module k V2] [inst_6 : AddTorsor V2 P2] {f g : P1 →ᵃ[k] P2}, (∀ (p : P1), f p = g p) → f = g

Two affine maps are equal if they coerce to the same function.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineMap

Cited by

19 results in Mathlib

Foundations

Depth 27 from the axioms · uses Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor