/*  This is a proof plan for theorem:
    zerotimes: []==>x:pnat=>y:pnat=>times(x,y)=0 in pnat=>x=0 in pnat\y=0 in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1090ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>times(x,y)=0 in pnat=>x=0 in pnat\y=0 in pnat,zerotimes,1090,ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(elementary(intro(new[y])then[intro(new[v0])then[intro(left)then[identity,wfftacs],wfftacs],wfftacs])),step_case(ripple(direction_out,wave(direction_out,[1,1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1],[zeroplus,imp(left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,=>,[1],v1)]))then elementary(intro(new[y])then[intro(new[v2])then[elim(v2)then elim(v3)then[intro(right)then[hyp(v4),wfftacs],intro(right)then[hyp(v4),wfftacs]],wfftacs],wfftacs])))])]),dplan).
