/*  This is a proof plan for theorem:
    comp: []==>a:pnat=>b:pnat=>plus(a,b)=plus(b,a)in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1710ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(a:pnat)-s(v0)]) then 
  [ind_strat([(b:pnat)-s(v0)]),
   ind_strat([(b:pnat)-s(v2)])
  ]

*/

proof_plan([]==>a:pnat=>b:pnat=>plus(a,b)=plus(b,a)in pnat,comp,1710,ind_strat(induction(lemma(pnat_primitive)-[(a:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1,1],[plus2,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],v1)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(b:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[2,1],[plus2,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],v1)]))then elementary(identity)))])]),ind_strat(induction(lemma(pnat_primitive)-[(b:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[plus2,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],v3)]))then elementary(identity)))])])],dplan).
