Theorem If (u,v)∈Tmin If exists (u′,v′)∈Tmin connects u∈S,v∈V−S AKA, Tmin without (u′,v′) disconnects and (u,v) would reconnect If weight(u,v)≤weight(u′,v′) Then. Tmin′=Tmin−{(u′,v′)}+{(u,v)}