let X be ARS ; :: thesis: for x, y being Element of X st x <<>> y holds
x <=*=> y
let x, y be Element of X; :: thesis: ( x <<>> y implies x <=*=> y )
assume A1: x <<>> y ; :: thesis: x <=*=> y
consider u being Element of X such that
A2: ( x <=*= u & u =*=> y ) by A1;
A3: ( x <=*=> u & u <=*=> y ) by A2, Lm3;
thus x <=*=> y by A3, Th7; :: thesis: verum