let AFV be WeakAffVect; :: thesis: for o being Element of AFV
for a being Element of (GroupVect AFV,o) holds a + (0. (GroupVect AFV,o)) = a
let o be Element of AFV; :: thesis: for a being Element of (GroupVect AFV,o) holds a + (0. (GroupVect AFV,o)) = a
let a be Element of (GroupVect AFV,o); :: thesis: a + (0. (GroupVect AFV,o)) = a
reconsider a9 = a as Element of AFV ;
reconsider x9 = a + (0. (GroupVect AFV,o)) as Element of AFV ;
x9 = Padd o,a9,o by Def7;
then o,a9 // o,x9 by Def5;
hence a + (0. (GroupVect AFV,o)) = a by Th5; :: thesis: verum