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

    Time taken to find plan: 1680ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(z:pnat)-s(v0)]) then 
  generalise(plus(v0,x),v2:pnat) then 
    ind_strat([(v2:pnat)-s(v4),(y:pnat)-s(v3)])

*/

proof_plan([]==>x:pnat=>y:pnat=>z:pnat=>greater(x,y)=>greater(plus(z,x),y),greaterplus,1680,ind_strat(induction(lemma(pnat_primitive)-[(z:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])then[intro(new[y])then[intro(new[v0])then[hyp(v0),wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2],[plus2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,=>,[],v1)]))))])])then[generalise(plus(v0,x),v2:pnat)then[ind_strat(induction(lemma(pairs)-[(v2:pnat)-s(v4),(y:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1],[greater1,equ(u(1),left)])]))then[elementary(intro(new[x])then[intro(new[v4])then[elim(v4),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([2],[greater2,equ(u(1),left)])]))then[elementary(intro(new[x])then[intro(new[v4])then[istrue,wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1],[greater3,equ(u(1),left)],[])then[unblock_then_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[2],[greater3,equ(u(1),left)],[]))])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v5))])])]],dplan).
