/*  This is a proof plan for theorem:
    expplus: []==>n:pnat=>i:pnat=>j:pnat=>exp(n,plus(i,j))=times(exp(n,i),exp(n,j))in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 4220ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(i:pnat)-s(v0)]) then 
  generalise(exp(n,j),v2:pnat) then 
    generalise(exp(n,v0),v3:pnat) then 
      ind_strat([(n:pnat)-s(v4)])

*/

proof_plan([]==>n:pnat=>i:pnat=>j:pnat=>exp(n,plus(i,j))=times(exp(n,i),exp(n,j))in pnat,expplus,4220,ind_strat(induction(lemma(pnat_primitive)-[(i:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1,1],[plus1,equ(pnat,left)]),reduction([1,2,1],[exp1,equ(pnat,left)]),reduction([2,1],[times2,equ(pnat,left)]),reduction([1,2,1],[times1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[n])then[intro(new[j])then[identity,wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[exp2,equ(pnat,left)],[])then[wave(direction_out,[2,1,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[exp2,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,in,[2],v1)]))))])])then[generalise(exp(n,j),v2:pnat)then[generalise(exp(n,v0),v3:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(n:pnat)-s(v4)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)]),reduction([1,2,1],[times1,equ(pnat,left)]),reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(intro(new[v3])then[intro(new[v2])then[intro(new[j])then[identity,wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[2,1],[disttwo,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],v5)]))then elementary(intro(new[v3])then[intro(new[v2])then[intro(new[j])then[identity,wfftacs],wfftacs],wfftacs])))])])]]],dplan).
