/*  This is a proof plan for theorem:
    lesseq: []==>x:pnat=>y:pnat=>((x=y in pnat=>void)#leq(x,y))=>less(x,y)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 600ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:pnat)-s(v1),(y:pnat)-s(v0)])

*/

proof_plan([]==>x:pnat=>y:pnat=>((x=y in pnat=>void)#leq(x,y))=>less(x,y),lesseq,600,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[leq1,equ(u(1),left)]),reduction([2],[lesszero,equiv(left)])]))then[elementary(intro(new[v1])then[intro(new[v2])then[elim(v1)then elim(v3)then[hyp(v2),hyp(v6)],wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([2,1],[leqzero,equiv(left)]),reduction([2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v1])then[elim(v1)then elim(v2)then[hyp(v3),hyp(v5)],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[less3,equ(u(1),left)],[])then[wave(direction_out,[2,1],[leq3,equ(u(1),left)],[])then[wave(direction_out,[1,1,1],[cnc_s,imp(right)],[])]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])]),dplan).
