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 Th11
.=
(quotadd I) . (v,u)
by Def12
;
hence
(quotadd I) . (u,v) = (quotadd I) . (v,u)
; verum