/*  This is a proof plan for theorem:
    times2right: []==>x:pnat=>y:pnat=>times(x,s(y))=plus(x,times(x,y))in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 3380ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>times(x,s(y))=plus(x,times(x,y))in pnat,times2right,3380,ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)]),reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(intro(new[y])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[2,1,2,1],[times2,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[generalise(times(v0,y),v2:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v0:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([1,2,1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[plus2,equ(pnat,left)],[])then[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],v4)]))then elementary(intro(new[v2])then[intro(new[y])then[identity,wfftacs],wfftacs])))])])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)]),reduction([1,2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[plus2,equ(pnat,left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,in,[1],v4)]))then elementary(intro(new[y])then[identity,wfftacs])))])])]]],dplan).
