let I be non degenerated commutative domRing-like Ring; for u, v being Element of Quot. I holds (quotadd I) . u,v = (quotadd I) . v,u
let u, v be Element of Quot. I; (quotadd I) . u,v = (quotadd I) . v,u
(quotadd I) . u,v =
qadd u,v
by Def12
.=
qadd v,u
by Th13
.=
(quotadd I) . v,u
by Def12
;
hence
(quotadd I) . u,v = (quotadd I) . v,u
; verum