/*  This is a proof plan for theorem:
    plusgeq2: []==>x:pnat=>y:pnat=>geq(plus(x,y),y)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 2030ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>geq(plus(x,y),y),plusgeq2,2030,ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1],[plus2right,equ(pnat,right)],[])])then[idtac])])then[ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([],[geqzero,equiv(left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[],[geq3,equ(u(1),left)],[]))then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),ind_strat(induction(lemma(pnat_primitive)-[(v0:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[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,geq,[],v3)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v2)])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),idtac])then wave(direction_out,[],[geq3,equ(u(1),left)],[])))then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v3))])]),generalise(plus(v2,s(y)),v4:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v4:pnat)-s(v5)])then[base_case(sym_eval(normalize_term([reduction([],[geq1,equ(u(1),left)])]))then[elementary(intro(new[y])then[istrue,wfftacs])]),step_case(ripple(direction_out,unblock_then_wave(direction_out,unblock_lazy([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,v6))])])]]],dplan).
