let E be set ; :: thesis: for a, b being Element of E ^omega st ( a ^ b = a or b ^ a = a ) holds
b = {}
let a, b be Element of E ^omega ; :: thesis: ( ( a ^ b = a or b ^ a = a ) implies b = {} )
assume A1: ( a ^ b = a or b ^ a = a ) ; :: thesis: b = {}
per cases ( a ^ b = a or b ^ a = a ) by A1;
suppose A2: a ^ b = a ; :: thesis: b = {}
len (a ^ b) = (len a) + (len b) by AFINSQ_1:17;
hence b = {} by A2; :: thesis: verum
end;
suppose A3: b ^ a = a ; :: thesis: b = {}
len (b ^ a) = (len b) + (len a) by AFINSQ_1:17;
hence b = {} by A3; :: thesis: verum
end;
end;