/*  This is a proof plan for theorem:
    zerotimes2: []==>x:pnat=>y:pnat=>y=0 in pnat=>times(x,y)=0 in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 670ms
    Environment:
    []
 */

/* This is the pretty-printed form
normalize(...) then 
  base_case(...) then 
    ind_strat([(x:pnat)-s(v0)]) then 
      generalise(times(v0,0),v2:pnat) then 
        ind_strat([(v2:pnat)-s(v3)])

*/

proof_plan([]==>x:pnat=>y:pnat=>y=0 in pnat=>times(x,y)=0 in pnat,zerotimes2,670,normalize([normal(univ_intro),normal(univ_intro),normal(imply_intro)])then[base_case(sym_eval(equal(v0,right)))then[ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1],[times2,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,[],v1)]))))])])then[generalise(times(v0,0),v2:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),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(right,[weak_fertilize(right,in,[1],v4)]))then elementary(identity)))])])]]]],dplan).
