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

    Time taken to find plan: 6940ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(a:int list)-v1::v0]) then 
  [ind_strat([(b:int list)-v1::v0]) then 
     generalise(rev(v0),v3:int list) then 
       ind_strat([(v3:int list)-v5::v4]),
   generalise(rev(v0),v3:int list) then 
     ind_strat([(b:int list)-v5::v4]) then 
       generalise(app(rev(v4),v5::nil),v7:int list) then 
         ind_strat([(v7:int list)-v9::v8])
  ]

*/

proof_plan([]==>a:int list=>b:int list=>rev(app(a,b))=app(rev(b),rev(a))in int list,dist_rev_app,6940,ind_strat(induction(lemma(list_primitive)-[(a:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[app1,equ(int list,left)]),reduction([2,2,1],[rev1,equ(int list,left)])]))),step_case(ripple(direction_out,wave(direction_out,[2,2,1],[rev2,equ(int list,left)],[])then[wave(direction_out,[1,1,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1],[rev2,equ(int list,left)],[])]])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,in,[1],v2)]))))])])then[ind_strat(induction(lemma(list_primitive)-[(b:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1],[rev1,equ(int list,left)]),reduction([1,2,1],[rev1,equ(int list,left)]),reduction([2,1],[app1,equ(int list,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1],[rev2,equ(int list,left)],[])then[wave(direction_out,[1,2,1],[rev2,equ(int list,left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,in,[1],v2)]))))])])then[generalise(rev(v0),v3:int list)then[ind_strat(induction(lemma(list_primitive)-[(v3:int list)-v5::v4])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[app1,equ(int list,left)]),reduction([1,1],[app1,equ(int list,left)]),reduction([1,2,1],[app1,equ(int list,left)]),reduction([2,1],[app2,equ(int list,left)]),reduction([2,2,1],[app1,equ(int list,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[app2,equ(int list,left)],[])then[wave(direction_out,[2,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1],[app2,equ(int list,left)],[])]]])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[2],v6)]))then elementary(identity)))])])]],generalise(rev(v0),v3:int list)then[ind_strat(induction(lemma(list_primitive)-[(b:int list)-v5::v4])then[base_case(sym_eval(normalize_term([reduction([1,1,1,1],[rev1,equ(int list,left)]),reduction([1,1,1],[app1,equ(int list,left)]),reduction([1,2,1],[rev1,equ(int list,left)]),reduction([2,1],[app1,equ(int list,left)])]))then[elementary(intro(new[v3])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[rev2,equ(int list,left)],[])then[wave(direction_out,[1,1,1,1],[rev2,equ(int list,left)],[])])then[idtac])])then[generalise(app(rev(v4),v5::nil),v7:int list)then[ind_strat(induction(lemma(list_primitive)-[(v7:int list)-v9::v8])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[app1,equ(int list,left)]),reduction([2,1],[app1,equ(int list,left)])]))then[elementary(intro(new[v3])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1],[app2,equ(int list,left)],[])]])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[2],v10)]))then elementary(intro(new[v3])then[identity,wfftacs])))])])]]]],dplan).
