/*  This is a proof plan for theorem:
    notlesstrans2: []==>x:pnat=>y:pnat=>z:pnat=>(less(x,z)#leq(y,x))=>less(y,z)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 2260ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:pnat)-s(v1),(y:pnat)-s(v0)]) then 
  [normalize(...) then 
     base_case(...),
   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(x,z)#leq(y,x))=>less(y,z),notlesstrans2,2260,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[leqzero,equiv(left)])]))),base_case(sym_eval(normalize_term([reduction([2,1],[leq1,equ(u(1),left)])]))),step_case(ripple(direction_out,wave(direction_out,[2,1],[leq3,equ(u(1),left)],[]))then[idtac])])then[normalize([normal(univ_intro),normal(imply_intro),normal(conjunct_elim(v1,[v2,v3]))])then[base_case(sym_eval(equal(v3,right))then[elementary(hyp(v2))])],ind_strat(induction(lemma(pairs)-[(v0:pnat)-s(v2),(z:pnat)-s(v1)])then[base_case(elementary(intro(new[v2])then[elim(v2)then hyp(v3),wfftacs])),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[v2])then[elim(v2)then hyp(v3),wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[less3,equ(u(1),left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,=>,[],v3)]))))])])then[base_case(sym_eval(normalize_term([reduction([2],[less2,equ(u(1),left)])]))then[elementary(intro(new[v4])then[istrue,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).
