X Y -> Z
set set set
definition
let X , Y be set;
func X Y -> set
means
:N: x
Cit iffx
CX & xCY;existence ......;
uniqueness
proof
end;
end;
x C A1 <=> x C X & x C Y
x C A2 <=> x C X & x C Y
A1 = A2
uniqueness
proof
let A1,A2 be set such that
A1: x
CA1 iff xCX & xCYand
A2: x
CA2 iff xCX & xCY;now let y;
y
CA1 iff yCX & yCY by A1;hence y
CA1 iff yCA2 by A2;end;
hence A1=A2 by TARSKI:2;
In short, when we bring in the two sets A1 and A2 that satisfy this condition, by demonstrating the equality of these two sets, the uniqueness is in fact demonstrated.