:: deftheorem Def7 defines B_Cut JORDAN3:def 7 :
for f being FinSequence of (TOP-REAL 2)
for p, q being Point of (TOP-REAL 2) holds
( ( ( ( p in L~ f & q in L~ f & Index (p,f) < Index (q,f) ) or ( Index (p,f) = Index (q,f) & LE p,q,f /. (Index (p,f)),f /. ((Index (p,f)) + 1) ) ) implies B_Cut (f,p,q) = R_Cut ((L_Cut (f,p)),q) ) & ( ( p in L~ f & q in L~ f & Index (p,f) < Index (q,f) ) or ( Index (p,f) = Index (q,f) & LE p,q,f /. (Index (p,f)),f /. ((Index (p,f)) + 1) ) or B_Cut (f,p,q) = Rev (R_Cut ((L_Cut (f,q)),p)) ) );