/*  This is a proof plan for theorem:
    ordered_cons: []==>x:int=>y:int list=>ordered(x::y)=>ordered(y)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1700ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(y:int list)-v0::v2::v1]) then 
  [base_case(...),
   base_case(...),
   base_case(...)
  ]

*/

proof_plan([]==>x:int=>y:int list=>ordered(x::y)=>ordered(y),ordered_cons,1700,ind_strat(induction(lemma(list_ind)-[(y:int list)-v0::v2::v1])then[base_case(sym_eval(normalize_term([reduction([1],[ordered2,equ(u(1),left)]),reduction([2],[ordered1,equ(u(1),left)])]))then[elementary(intro(new[x])then[intro(new[v0])then[hyp(v0),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([2],[ordered2,equ(u(1),left)])])then[casesplit(disjunction([v0<x=>void,v0<x]))then[normalize_term([reduction([1],[ordered4,equ(u(1),left)]),reduction([1],[ordered2,equ(u(1),left)])]),normalize_term([reduction([1],[ordered3,equ(u(1),left)])])]])then[elementary(intro(new[v2])then[hyp(v2),wfftacs]),elementary(intro(new[v2])then[istrue,wfftacs])]),step_case(ripple(direction_out,casesplit(disjunction([v2<v0=>void,v2<v0]))then[wave(direction_out,[2],[ordered4,equ(u(1),left)],[])then[casesplit(disjunction([v0<x=>void,v0<x]))then[wave(direction_out,[1],[ordered4,equ(u(1),left)],[]),wave(direction_out,[1],[ordered3,complementary,equ(u(1),left)],[])]],wave(direction_out,[2],[ordered3,complementary,equ(u(1),left)],[])then[casesplit(disjunction([v0<x=>void,v0<x]))then[idtac,idtac]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v3)),idtac,idtac,idtac])])then[base_case(elementary(intro(new[v6])then[elim(v6),wfftacs])),base_case(sym_eval(normalize_term([reduction([1],[ordered4,equ(u(1),left)]),reduction([1],[ordered3,equ(u(1),left)])]))then[elementary(intro(new[v6])then[hyp(v6),wfftacs])]),base_case(sym_eval(normalize_term([reduction([1],[ordered3,equ(u(1),left)])]))then[elementary(intro(new[v6])then[hyp(v6),wfftacs])])],dplan).
