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

    Time taken to find plan: 600ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:int=>y:int list=>member(x,insert(x,y)),memins,600,ind_strat(induction(lemma(list_primitive)-[(y:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([2],[insert1,equ(int list,left)]),reduction([],[member2,equ(u(1),left)])]))then[elementary(intro(new[x])then[istrue,wfftacs])]),step_case(ripple(direction_out,casesplit(disjunction([x<v1=>void,x<v1]))then[wave(direction_out,[2],[insert3,equ(int list,left)],[])then[casesplit(disjunction([x=v1 in int=>void,x=v1 in int]))then[wave(direction_out,[],[member3,equ(u(1),left)],[]),wave(direction_out,[],[member2,complementary,equ(u(1),left)],[])]],wave(direction_out,[2],[insert2,complementary,equ(int list,left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2)),idtac,idtac])])then[base_case(elementary(istrue)),base_case(sym_eval(normalize_term([reduction([],[member2,equ(u(1),left)])]))then[elementary(istrue)])],dplan).
