load ui

load tree

--- mcc(A,mktree(G)) = mcc(A,G) ---

--- Induction base ---

(goal GRAPH |- eq mcc(A:Vertex,mktree(nil)) = mcc(A:Vertex,nil) ;)

(apply TC RD .)

--- Induction step ---

(fmod TH1 is ---> fth TH1
 pr GRAPH . 
 op g : -> Graph .
 var A : Vertex .
 eq [IH]: mcc(A,mktree(g)) = mcc(A,g) .
endfm)

(goal TH1 |- eq mcc(A:Vertex,mktree(< B:Vertex, C:Vertex > ; g)) = mcc(A:Vertex,< B:Vertex, C:Vertex > ; g) ;)

(apply TC CA CA-1 RD .)