let S be satisfying_Tarski-model TarskiGeometryStruct ; for a, b, c, d being POINT of S st between a,b,d & between b,c,d holds
between a,c,d
let a, b, c, d be POINT of S; ( between a,b,d & between b,c,d implies between a,c,d )
assume A1:
( between a,b,d & between b,c,d )
; between a,c,d
then
between a,b,c
by Satz3p5p1;
hence
between a,c,d
by A1, Satz3p7p1; verum