/*  This is a proof plan for theorem:
    doubletimes1: []==>n:pnat=>double(n)=times(s(s(0)),n)in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 2900ms
    Environment:
    []
 */

/* This is the pretty-printed form
base_case(...) then 
  ind_strat([(n:pnat)-s(v0)]) then 
    ind_strat([(v0:pnat)-s(v2)]) then 
      generalise(s(v2),v4:pnat) then 
        ind_strat([(v2:pnat)-s(v5)])

*/

proof_plan([]==>n:pnat=>double(n)=times(s(s(0)),n)in pnat,doubletimes1,2900,base_case(sym_eval(normalize_term([reduction([2,1],[times2,equ(pnat,left)]),reduction([1,2,1],[times2,equ(pnat,left)]),reduction([1,1,2,1],[times1,equ(pnat,left)]),reduction([1,2,1],[plus1,equ(pnat,left)])])))then[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],[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],[double2,equ(pnat,left)],[])then[wave(direction_out,[],[cnc_s,imp(right)],[])]])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)-[(v0: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_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[idtac])])then[generalise(s(v2),v4:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v5)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[v4])then[identity,wfftacs])]),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_wave(direction_out,unblock_lazy([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,v6))])])]]]],dplan).
