let f be FinSequence of (TOP-REAL 2); :: thesis: for p, q being Point of (TOP-REAL 2) st f is being_S-Seq & p in L~ f & q in L~ f & p <> q holds
B_Cut (f,p,q) is being_S-Seq
let p, q be Point of (TOP-REAL 2); :: thesis: ( f is being_S-Seq & p in L~ f & q in L~ f & p <> q implies B_Cut (f,p,q) is being_S-Seq )
assume that
A1: f is being_S-Seq and
A2: p in L~ f and
A3: q in L~ f and
A4: p <> q ; :: thesis: B_Cut (f,p,q) is being_S-Seq
B_Cut (f,p,q) is_S-Seq_joining p,q by A1, A2, A3, A4, Th36;
hence B_Cut (f,p,q) is being_S-Seq ; :: thesis: verum