/*  This is a proof plan for theorem:
    greatertrans: []==>x:pnat=>y:pnat=>z:pnat=>(greater(x,y)#greater(y,z))=>greater(x,z)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1680ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:pnat)-s(v1),(y:pnat)-s(v0)]) then 
  ind_strat([(z:pnat)-s(v3)])

*/

proof_plan([]==>x:pnat=>y:pnat=>z:pnat=>(greater(x,y)#greater(y,z))=>greater(x,z),greatertrans,1680,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[greater1,equ(u(1),left)]),reduction([2],[greater1,equ(u(1),left)])]))then[elementary(intro(new[z])then[intro(new[v1])then[elim(v1)then hyp(v2),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([1,1],[greaterzero,equiv(left)]),reduction([2,1],[greater1,equ(u(1),left)])]))then[elementary(intro(new[z])then[intro(new[v1])then[elim(v1)then elim(v3),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[greater3,equ(u(1),left)],[]))then[idtac])])then[ind_strat(induction(lemma(pnat_primitive)-[(z:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([2,1],[greaterzero,equiv(left)]),reduction([2],[greaterzero,equiv(left)])]))then[elementary(intro(new[v3])then[intro(new[v4])then[clam_arith(v4:s(v1)=0 in pnat),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[greater3,equ(u(1),left)],[])then[wave(direction_out,[2,1],[greater3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])])],dplan).
