let x1, x2, x3, y1, y2 be object ; [:{x1,y1},{x2,y2},{x3}:] = {[x1,x2,x3],[y1,x2,x3],[x1,y2,x3],[y1,y2,x3]}
thus [:{x1,y1},{x2,y2},{x3}:] =
[:[:{x1,y1},{x2,y2}:],{x3}:]
by ZFMISC_1:def 3
.=
[:{[x1,x2],[x1,y2],[y1,x2],[y1,y2]},{x3}:]
by Th17
.=
[:({[x1,x2],[x1,y2]} \/ {[y1,x2],[y1,y2]}),{x3}:]
by ENUMSET1:5
.=
[:{[x1,x2],[x1,y2]},{x3}:] \/ [:{[y1,x2],[y1,y2]},{x3}:]
by ZFMISC_1:97
.=
{[[x1,x2],x3],[[x1,y2],x3]} \/ [:{[y1,x2],[y1,y2]},{x3}:]
by ZFMISC_1:30
.=
{[[x1,x2],x3],[[x1,y2],x3]} \/ {[[y1,x2],x3],[[y1,y2],x3]}
by ZFMISC_1:30
.=
{[x1,x2,x3],[x1,y2,x3],[y1,x2,x3],[[y1,y2],x3]}
by ENUMSET1:5
.=
{[x1,x2,x3],[y1,x2,x3],[x1,y2,x3],[y1,y2,x3]}
by ENUMSET1:62
; verum