/*  This is a proof plan for theorem:
    doubletimes2: []==>n:pnat=>double(n)=times(n,s(s(0)))in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1690ms
    Environment:
    []
 */

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

*/

proof_plan([]==>n:pnat=>double(n)=times(n,s(s(0)))in pnat,doubletimes2,1690,ind_strat(induction(lemma(pnat_primitive)-[(n:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[double1,equ(pnat,left)]),reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[2,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[double2,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[generalise(double(v0),v2:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])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_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[],[cnc_s,imp(right)],[]))])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v4))])])]],dplan).
