load tree

--- nocycle(mktree(G)) = true ---

--- Induction base ---

(goal GRAPH |- eq nocycle(mktree(nil)) = true ;)

(apply RD .)

--- Induction step ---

(fmod TH3 is ---> fth TH3
 pr GRAPH . 
 op g : -> Graph .
 var A : Vertex . var G : Graph .
 eq [TH1]: mcc(A,mktree(G)) = mcc(A,G) .
 eq [TH2]: nomcc(mktree(G)) = nomcc(G) .
 eq [IH]:  nocycle(mktree(g)) = true .
endfm)

(goal TH3 |- eq nocycle(mktree(< A:Vertex,B:Vertex > ; g)) = true ;)

(apply TC CA RD .)