/*  This is a proof plan for theorem:
    comapp: []==>x:int list=>y:int list=>length(app(x,y))=length(app(y,x))in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 2080ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:int list)-v1::v0]) then 
  [ind_strat([(y:int list)-v1::v0]),
   ind_strat([(y:int list)-v4::v3])
  ]

*/

proof_plan([]==>x:int list=>y:int list=>length(app(x,y))=length(app(y,x))in pnat,comapp,2080,ind_strat(induction(lemma(list_primitive)-[(x:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[app1,equ(int list,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1,1,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1],[length2,equ(pnat,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)-[(y:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1,1],[length1,equ(pnat,left)]),reduction([1,2,1],[app1,equ(int list,left)]),reduction([2,1],[length1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1],[length2,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[app2,equ(int list,left)],[])then[wave(direction_out,[2,1],[length2,equ(pnat,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,[1],v2)]))then elementary(identity)))])]),ind_strat(induction(lemma(list_primitive)-[(y:int list)-v4::v3])then[base_case(sym_eval(normalize_term([reduction([1,1,1,1],[app1,equ(int list,left)]),reduction([1,2,1],[app1,equ(int list,left)]),reduction([2,1],[length2,equ(pnat,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],[length2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1,1],[app2,equ(int list,left)],[])then[wave(direction_out,[1,1,1],[length2,equ(pnat,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,[1],v5)]))then elementary(identity)))])])],dplan).
