let F1, F2 be Function of [:REAL,REAL:],REAL; :: thesis: ( ( for x, y being Real holds F1 . (x,y) = |.(x - y).| ) & ( for x, y being Real holds F2 . (x,y) = |.(x - y).| ) implies F1 = F2 )
assume that
A2: for x, y being Real holds F1 . (x,y) = |.(x - y).| and
A3: for x, y being Real holds F2 . (x,y) = |.(x - y).| ; :: thesis: F1 = F2
for x, y being Element of REAL holds F1 . (x,y) = F2 . (x,y)

proof

let x, y be Element of REAL ; :: thesis: F1 . (x,y) = F2 . (x,y)
thus F1 . (x,y) = |.(x - y).| by A2
.= F2 . (x,y) by A3 ; :: thesis: verum

end;

hence F1 = F2 ; :: thesis: verum