set qa = QuotOSAlg (U1,(OSCng F));
set cqa = the Sorts of (QuotOSAlg (U1,(OSCng F)));
set u1 = the Sorts of U1;
set u2 = the Sorts of U2;
let H, G be Function of ( the Sorts of (QuotOSAlg (U1,(OSCng F))) . s),( the Sorts of U2 . s); ( ( for x being Element of the Sorts of U1 . s holds H . (OSClass ((OSCng F),x)) = (F . s) . x ) & ( for x being Element of the Sorts of U1 . s holds G . (OSClass ((OSCng F),x)) = (F . s) . x ) implies H = G )
assume that
A9:
for a being Element of the Sorts of U1 . s holds H . (OSClass ((OSCng F),a)) = (F . s) . a
and
A10:
for a being Element of the Sorts of U1 . s holds G . (OSClass ((OSCng F),a)) = (F . s) . a
; H = G
A11:
the Sorts of (QuotOSAlg (U1,(OSCng F))) . s = OSClass ((OSCng F),s)
by Def11;
for x being object st x in the Sorts of (QuotOSAlg (U1,(OSCng F))) . s holds
H . x = G . x
hence
H = G
by FUNCT_2:12; verum