/*  This is a proof plan for theorem:
    doublehalf: []==>n:pnat=>even(n)=>double(half(n))=n in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 430ms
    Environment:
    []
 */

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

*/

proof_plan([]==>n:pnat=>even(n)=>double(half(n))=n in pnat,doublehalf,430,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([1,1,1,2],[half1,equ(pnat,left)]),reduction([1,1,2],[double1,equ(pnat,left)])]))then[elementary(intro(new[v0])then[identity,wfftacs])]),base_case(sym_eval(normalize_term([reduction([1],[even2,equ(u(1),left)]),reduction([1,1,1,2],[half2,equ(pnat,left)]),reduction([1,1,2],[double1,equ(pnat,left)])]))then[elementary(intro(new[v0])then[elim(v0),wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1],[even3,equ(u(1),left)],[])then[wave(direction_out,[1,1,1,2],[half3,equ(pnat,left)],[])then[wave(direction_out,[1,1,2],[double2,equ(pnat,left)],[])then[wave(direction_out,[2],[cnc_s,imp(right)],[])then[wave(direction_out,[2],[cnc_s,imp(right)],[])]]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),dplan).
