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

    Time taken to find plan: 240ms
    Environment:
    []
 */

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

*/

proof_plan([]==>x:pnat=>y:pnat=>leq(min(x,y),max(x,y)),minmax,240,ind_strat(induction(lemma(pairs)-[(x:pnat)-s(v1),(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1],[min1,equ(pnat,left)]),reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),base_case(sym_eval(normalize_term([reduction([1],[min2,equ(pnat,left)]),reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,wave(direction_out,[2],[max3,equ(pnat,left)],[])then[wave(direction_out,[1],[min3,equ(pnat,left)],[])then[wave(direction_out,[],[leq3,equ(u(1),left)],[])]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2))])]),dplan).
