/*  This is a proof plan for theorem:
    lessleq1: []==>x:pnat=>y:pnat=>(leq(x,y)=>void)=>less(y,x)
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 270ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>(leq(x,y)=>void)=>less(y,x),lessleq1,270,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[leq1,equ(u(1),left)]),reduction([2],[less1,equ(u(1),left)])]))then[elementary(intro(new[v1])then[elim(v1)then[istrue,hyp(v2)],wfftacs])]),base_case(sym_eval(normalize_term([reduction([1,1],[leqzero,equiv(left)]),reduction([2],[lesszero,equiv(left)])]))then[elementary(intro(new[v1])then[hyp(v1),wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2],[less3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[leq3,equ(u(1),left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])]),dplan).
