/*  This is a proof plan for theorem:
    lesstrans1: []==>x:pnat=>y:pnat=>z:pnat=>((less(z,x)=>void)#less(x,y)=>void)=>less(z,y)=>void
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 2820ms
    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(z,x)=>void)#less(x,y)=>void)=>less(z,y)=>void,lesstrans1,2820,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[less1,equ(u(1),left)])]))),base_case(sym_eval(normalize_term([reduction([1,2,1],[less1,equ(u(1),left)]),reduction([1,2],[less1,equ(u(1),left)])]))then[elementary(intro(new[z])then[intro(new[v1])then[intro(new[v2])then[hyp(v2),wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[less3,equ(u(1),left)],[]))then[idtac])])then[ind_strat(induction(lemma(pairs)-[(v0:pnat)-s(v2),(z:pnat)-s(v1)])then[base_case(sym_eval(normalize_term([reduction([1,2,1],[less1,equ(u(1),left)]),reduction([1,2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v2])then[intro(new[v3])then[hyp(v3),wfftacs],wfftacs])]),base_case(elementary(intro(new[v2])then[intro(new[v3])then[elim(v2)then elim(v4)then[elim(v5)then[hyp(v3),hyp(v7)],hyp(v7)],wfftacs],wfftacs])),step_case(ripple(direction_out,wave(direction_out,[1,2],[less3,equ(u(1),left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,=>,[],v3)]))))])])then[base_case(sym_eval(normalize_term([reduction([1,2,1],[less2,equ(u(1),left)])]))then[elementary(intro(new[v4])then[intro then[intro(new[v5])then[hyp(v5),wfftacs],intro(new[v5])then[elim(v4)then elim(v6)then[elim(v7)then[istrue,hyp(v9)],hyp(v9)],wfftacs]],wfftacs])])],ind_strat(induction(lemma(pnat_primitive)-[(z:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[less2,equ(u(1),left)]),reduction([1,2],[less2,equ(u(1),left)])]))then[elementary(intro(new[v3])then[intro(new[v4])then[elim(v3)then elim(v5)then[hyp(v4),hyp(v8)],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2],[less3,equ(u(1),left)],[])then[wave(direction_out,[1,1,1],[less3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])])],dplan).
