let x, y be set ; :: thesis: ( <*x*>,<*y*> are_c=-comparable implies x = y )
assume A1: <*x*>,<*y*> are_c=-comparable ; :: thesis: x = y
( len <*x*> = 1 & len <*y*> = 1 ) by FINSEQ_1:57;
then A3: <*x*> = <*y*> by A1, Th19;
<*x*> . 1 = x by FINSEQ_1:57;
hence x = y by A3, FINSEQ_1:57; :: thesis: verum