let D be non empty set ; for G1, G2, G3 being Element of PFuncs (D,REAL) holds Sum <*G1,G2,G3*> = (G1 + G2) + G3
let G1, G2, G3 be Element of PFuncs (D,REAL); Sum <*G1,G2,G3*> = (G1 + G2) + G3
thus Sum <*G1,G2,G3*> =
Sum (<*G1,G2*> ^ <*G3*>)
by FINSEQ_1:43
.=
(Sum <*G1,G2*>) + G3
by Th20
.=
(G1 + G2) + G3
by Th23
; verum