/*  This is a proof plan for theorem:
    greaterplus2: []==>x:pnat=>y:pnat=>z:pnat=>greater(x,y)=>greater(plus(x,z),y)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1960ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>z:pnat=>greater(x,y)=>greater(plus(x,z),y),greaterplus2,1960,ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[greater1,equ(u(1),left)]),reduction([1,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[intro(new[z])then[intro(new[v0])then[elim(v0),wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2],[plus2,equ(pnat,left)],[]))then[idtac])])then[ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1],[greater2,equ(u(1),left)]),reduction([2],[greater2,equ(u(1),left)])]))then[elementary(intro(new[z])then[intro(new[v2])then[hyp(v2),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[greater3,equ(u(1),left)],[])then[wave(direction_out,[1],[greater3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])])],dplan).
