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

    Time taken to find plan: 5110ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>half(plus(x,x))=x in pnat,halfpnat,5110,ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([1,1],[half1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1,1],[plus2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v1)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(v0:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1,1,1,1],[plus1,equ(pnat,left)]),reduction([1,1],[half3,equ(pnat,left)]),reduction([],[cnc_s,imp(right)]),reduction([],[cnc_half,imp(right)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,1,2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1,1],[plus2,equ(pnat,left)],[])])then[idtac])])then[generalise(s(v2),v4:pnat)then[base_case(sym_eval(normalize_term([reduction([1,1],[half3,equ(pnat,left)]),reduction([],[cnc_s,imp(right)]),reduction([],[cnc_half,imp(right)])])))then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v5)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)]),reduction([],[cnc_s,imp(right)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[v4])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_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).
