/*  This is a proof plan for theorem:
    lesstrans3: []==>x:pnat=>y:pnat=>z:pnat=>(less(y,z)#less(x,y))=>less(x,z)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 2270ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:pnat)-s(v1),(y:pnat)-s(v0)]) then 
  [ind_strat([(v0:pnat)-s(v2),(z:pnat)-s(v1)]) then 
     base_case(...),
   ind_strat([(z:pnat)-s(v3)])
  ]

*/

proof_plan([]==>x:pnat=>y:pnat=>z:pnat=>(less(y,z)#less(x,y))=>less(x,z),lesstrans3,2270,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[lesszero,equiv(left)]),reduction([2],[lesszero,equiv(left)])]))),base_case(sym_eval(normalize_term([reduction([1,1],[lesszero,equiv(left)]),reduction([2,1],[less1,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,[2,1],[less3,equ(u(1),left)],[]))then[idtac])])then[ind_strat(induction(lemma(pairs)-[(v0:pnat)-s(v2),(z:pnat)-s(v1)])then[base_case(elementary(intro(new[v2])then[intro(new[v3])then[elim(v2)then elim(v5)then[identity,hyp(v7)],wfftacs],wfftacs])),base_case(sym_eval(normalize_term([reduction([1,1],[less1,equ(u(1),left)])]))then[elementary(intro(new[v2])then[intro(new[v3])then[elim(v2)then hyp(v4),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[less3,equ(u(1),left)],[]))then[idtac])])then[base_case(elementary(intro(new[v4])then[intro(new[v5])then[clam_arith(v5:s(v1)=0 in pnat),wfftacs],wfftacs]))],ind_strat(induction(lemma(pnat_primitive)-[(z:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1],[less1,equ(u(1),left)]),reduction([2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v3])then[elim(v3)then hyp(v4),wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[less3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[less3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])])],dplan).
