:: deftheorem Def7 defines OrtAfSp-like ANALMETR:def 8 :
for IT being non empty ParOrtStr holds
( IT is OrtAfSp-like iff ( AffinStruct(# the carrier of IT, the CONGR of IT #) is AffinSpace & ( for a, b, c, d, p, q, r, s being Element of IT holds
( ( a,b _|_ a,b implies a = b ) & a,b _|_ c,c & ( a,b _|_ c,d implies ( a,b _|_ d,c & c,d _|_ a,b ) ) & ( a,b _|_ p,q & a,b // r,s & not p,q _|_ r,s implies a = b ) & ( a,b _|_ p,q & a,b _|_ p,s implies a,b _|_ q,s ) ) ) & ( for a, b, c being Element of IT st a <> b holds
ex x being Element of IT st
( a,b // a,x & a,b _|_ x,c ) ) & ( for a, b, c being Element of IT ex x being Element of IT st
( a,b _|_ c,x & c <> x ) ) ) );