/*  This is a proof plan for theorem:
    evenm: []==>n:pnat=>m:pnat=>even(n)=>even(times(n,m))
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 1560ms
    Environment:
    []
 */

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

*/

proof_plan([]==>n:pnat=>m:pnat=>even(n)=>even(times(n,m)),evenm,1560,ind_strat(induction(lemma(pnat_primitive)-[(m:pnat)-s(v0)])then[idtac,step_case(ripple(direction_out,wave(direction_out,[1,2],[times2right,equ(pnat,left)],[])then[wave(direction_out,[2],[evenp,imp(right)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,=>,[2],v1)]))then elementary(intro(new[n])then[intro(new[v2])then[intro then[hyp(v2),hyp(v2)],wfftacs],wfftacs])))])])then[ind_strat(induction(lemma(twos)-[(n:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1],[even1,equ(u(1),left)]),reduction([1,2],[times1,equ(pnat,left)]),reduction([2],[even1,equ(u(1),left)])]))then[elementary(intro(new[v0])then[hyp(v0),wfftacs])]),base_case(sym_eval(normalize_term([reduction([1],[even2,equ(u(1),left)]),reduction([1,2],[times2,equ(pnat,left)]),reduction([1,1,2],[times1,equ(pnat,left)]),reduction([1,2],[plus1,equ(pnat,left)]),reduction([2],[even1,equ(u(1),left)])]))then[elementary(intro(new[v0])then[istrue,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1],[even3,equ(u(1),left)],[])then[wave(direction_out,[1,2],[times2,equ(pnat,left)],[])then[wave(direction_out,[2],[evenp,imp(right)],[])then[wave(direction_out,[1,1,2],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,2],[evenp,imp(right)],[])]]]])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,=>,[1,1],v1)])then ripple_and_cancel([unblock(wave_front,[2,2],[even1,equ(u(1),left)]),unblock(wave_front,[2,1,2],[even1,equ(u(1),left)])]))then elementary(intro(new[v2])then[intro then[intro then[hyp(v2),istrue],istrue],wfftacs])))])])],dplan).
