let a be Real; :: thesis: 0 <= a ^2

per cases ( a = 0 or a <> 0 ) ;

suppose a = 0 ; :: thesis: 0 <= a ^2

hence 0 <= a ^2 ; :: thesis: verum

end;

suppose a <> 0 ; :: thesis: 0 <= a ^2

hence 0 <= a ^2 by SQUARE_1:12; :: thesis: verum

end;

end;