/*  This is a proof plan for theorem:
    geqdoublehalf: []==>x:pnat=>geq(double(x),half(x))
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1230ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>geq(double(x),half(x)),geqdoublehalf,1230,ind_strat(induction(lemma(twos)-[(x:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1],[double1,equ(pnat,left)]),reduction([2],[half1,equ(pnat,left)]),reduction([],[geq1,equ(u(1),left)])]))then[elementary(istrue)]),base_case(sym_eval(normalize_term([reduction([1],[double2,equ(pnat,left)]),reduction([1,1,1],[double1,equ(pnat,left)]),reduction([2],[half2,equ(pnat,left)]),reduction([],[geq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,wave(direction_out,[2],[half3,equ(pnat,left)],[])then[wave(direction_out,[1],[double2,equ(pnat,left)],[])then[wave(direction_out,[],[geq3,equ(u(1),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,geq,[],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([],[geq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,unblock_then_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),unblock(meta_ripple,unused,unused),unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[],[geq3,equ(u(1),left)],[])))then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v4))])])]],dplan).
