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

    Time taken to find plan: 2200ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>z:pnat=>less(x,y)=>less(x,plus(y,z)),plusless,2200,ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[less1,equ(u(1),left)]),reduction([2,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])then[intro(new[z])then[intro(new[v0])then[elim(v0),wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,2],[plus2,equ(pnat,left)],[]))then[idtac])])then[ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([1],[less2,equ(u(1),left)]),reduction([2],[less2,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],[less3,equ(u(1),left)],[])then[wave(direction_out,[1],[less3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])])],dplan).
