/*  This is a proof plan for theorem:
    memapp3: []==>e:int=>l1:int list=>l2:int list=>(member(e,l1)\member(e,l2))=>member(e,app(l1,l2))
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1120ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(l1:int list)-v1::v0]) then 
  base_case(...)

*/

proof_plan([]==>e:int=>l1:int list=>l2:int list=>(member(e,l1)\member(e,l2))=>member(e,app(l1,l2)),memapp3,1120,ind_strat(induction(lemma(list_primitive)-[(l1:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1],[member1,equ(u(1),left)]),reduction([2,2],[app1,equ(int list,left)])]))then[elementary(intro(new[e])then[intro(new[l2])then[intro(new[v0])then[elim(v0)then[elim(v1),hyp(v2)],wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,2],[app2,equ(int list,left)],[])then[casesplit(disjunction([e=v1 in int=>void,e=v1 in int]))then[wave(direction_out,[2],[member3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[member3,equ(u(1),left)],[])],wave(direction_out,[2],[member2,complementary,equ(u(1),left)],[])]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2)),idtac])])then[base_case(elementary(intro(new[l2])then[intro(new[v4])then[istrue,wfftacs],wfftacs]))],dplan).
