/*  This is a proof plan for theorem:
    subsetunion: []==>a:int list=>b:int list=>subset(a,b)=>union(a,b)=b in int list
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1240ms
    Environment:
    []
 */

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

*/

proof_plan([]==>a:int list=>b:int list=>subset(a,b)=>union(a,b)=b in int list,subsetunion,1240,ind_strat(induction(lemma(list_primitive)-[(a:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1],[subset1,equ(u(1),left)]),reduction([1,1,2],[union1,equ(int list,left)])]))then[elementary(intro(new[b])then[intro(new[v0])then[identity,wfftacs],wfftacs])]),step_case(ripple(direction_out,casesplit(disjunction([member(v1,b)=>void,member(v1,b)]))then[wave(direction_out,[1,1,2],[union4,equ(int list,left)],[])then[wave(direction_out,[1],[subset2,complementary,equ(u(1),left)],[])],wave(direction_out,[1],[subset3,equ(u(1),left)],[])then[wave(direction_out,[1,1,2],[union3,equ(int list,left)],[])]])then[idtac,unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])])then[base_case(elementary(intro(new[v4])then[elim(v4),wfftacs]))],dplan).
