let OAS be OAffinSpace; :: thesis: OAS is satisfying_Gen_Par_Pasch
let a be Element of OAS; :: according to PASCH:def 3 :: thesis: for b, c, a', b', c' being Element of OAS st not LIN a,b,a' & a,a' '||' b,b' & a,a' '||' c,c' & Mid a,b,c & LIN a',b',c' holds
Mid a',b',c'
let b, c, a', b', c' be Element of OAS; :: thesis: ( not LIN a,b,a' & a,a' '||' b,b' & a,a' '||' c,c' & Mid a,b,c & LIN a',b',c' implies Mid a',b',c' )
assume ( not LIN a,b,a' & a,a' '||' b,b' & a,a' '||' c,c' & Mid a,b,c & LIN a',b',c' ) ; :: thesis: Mid a',b',c'
hence Mid a',b',c' by Th17; :: thesis: verum