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

    Time taken to find plan: 540ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>leq(half(x),x),leqhalf,540,ind_strat(induction(lemma(twos)-[(x:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1],[half1,equ(pnat,left)]),reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),base_case(sym_eval(normalize_term([reduction([1],[half2,equ(pnat,left)]),reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,wave(direction_out,[1],[half3,equ(pnat,left)],[])then[wave(direction_out,[],[leq3,equ(u(1),left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,leq,[],v1)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(v0:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,unblock_then_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[],[leq3,equ(u(1),left)],[])))then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v3))])])],dplan).
