let x1, x2, x3, y1, y2, y3 be object ; [:{x1,y1},{x2,y2},{x3,y3}:] = {[x1,x2,x3],[x1,y2,x3],[x1,x2,y3],[x1,y2,y3],[y1,x2,x3],[y1,y2,x3],[y1,x2,y3],[y1,y2,y3]}
A1: [:{[x1,x2],[x1,y2]},{x3,y3}:] =
{[[x1,x2],x3],[[x1,x2],y3],[[x1,y2],x3],[[x1,y2],y3]}
by Th17
.=
{[x1,x2,x3],[x1,y2,x3],[x1,x2,y3],[x1,y2,y3]}
by ENUMSET1:62
;
A2: [:{[y1,x2],[y1,y2]},{x3,y3}:] =
{[[y1,x2],x3],[[y1,x2],y3],[[y1,y2],x3],[[y1,y2],y3]}
by Th17
.=
{[y1,x2,x3],[y1,y2,x3],[y1,x2,y3],[y1,y2,y3]}
by ENUMSET1:62
;
thus [:{x1,y1},{x2,y2},{x3,y3}:] =
[:[:{x1,y1},{x2,y2}:],{x3,y3}:]
by ZFMISC_1:def 3
.=
[:{[x1,x2],[x1,y2],[y1,x2],[y1,y2]},{x3,y3}:]
by Th17
.=
[:({[x1,x2],[x1,y2]} \/ {[y1,x2],[y1,y2]}),{x3,y3}:]
by ENUMSET1:5
.=
{[x1,x2,x3],[x1,y2,x3],[x1,x2,y3],[x1,y2,y3]} \/ {[y1,x2,x3],[y1,y2,x3],[y1,x2,y3],[y1,y2,y3]}
by A1, A2, ZFMISC_1:97
.=
{[x1,x2,x3],[x1,y2,x3],[x1,x2,y3],[x1,y2,y3],[y1,x2,x3],[y1,y2,x3],[y1,x2,y3],[y1,y2,y3]}
by ENUMSET1:25
; verum