problem([]==>x:pnat=>leq(half(x),double(x)),
ind_strat(induction(lemma(twos)-[(x:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1],[half1,equ(pnat,left)]),reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),base_case(sym_eval(normalize_term([reduction([1],[half2,equ(pnat,left)]),reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,wave(direction_out,[2],[double2,equ(pnat,left)],[])then[wave(direction_out,[1],[half3,equ(pnat,left)],[])then[wave(direction_out,[],[leq3,equ(u(1),left)],[])then[wave(direction_out,[1,2],[double2,equ(pnat,left)],[])]]])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,leq,[],v1)]))))])]),lambda(x,su(lambda(v3,su(su(su(su(su(v8,[v7 of x],[v8]),[v6 of lambda(v0,lambda(v1,su(su(su(su(su(su(su(su(su(lambda(v5,lambda(v7,lambda(v6,su(su(su(su(su(su(su(su(su(su(su(su(v9,[v8 of v4],[v9]),[v2 of lambda(v8,su(su(v10,[v9 of v7],[v10]),[v8 of v1],[v9]))],[v8]),[v10 of leq(half(v0),s(s(s(double(v0)))))],[v2]),[v9 of leq(half(v0),s(s(s(double(v0)))))],[v10]),[v8 of leq(double(v0),s(s(s(double(v0)))))],[v9]),[v2 of leq(half(v0),double(v0))],[v8]),[term_of(ipc_dp_imp_e2)],[v2]),[v2 of double(v0)],[v3]),[v6 of half(v0)],[v2]),[v3 of s(s(s(double(v0))))],[v4]),[v2 of double(v0)],[v3]),[v5 of half(v0)],[v2]))of lambda(n,lambda(m,lambda(v2,v2))))of _107845)of atom(incomplete),[double2 of v0],[v2]),[term_of(double2)],[double2]),[v2 of s(double(s(v0)))],[v3]),[leq3 of half(v0)],[v2]),[term_of(leq3)],[leq3]),[half3 of v0],[v2]),[term_of(half3)],[half3]),[double2 of s(v0)],[v2]),[term_of(double2)],[double2])))],[v7]),[v5 of su(su(su(0,[leq1 of double(s(0))],[v0]),[term_of(leq1)],[leq1]),[term_of(half2)],[half2])],[v6]),[v4 of su(su(su(0,[leq1 of double(0)],[v0]),[term_of(leq1)],[leq1]),[term_of(half1)],[half1])],[v5]),[v3 of lambda(x,leq(half(x),double(x)))],[v4]))of v2,[term_of(twos)],[v2])),
[problem([x:pnat,v0:pnat,v1:leq(half(v0),double(v0))]==>leq(double(v0),s(s(s(double(v0))))),
 generalise(double(v0),v2:pnat),lambda(v2,su(v3,[v2 of double(v0)],[v3]))of _107372,
 [problem([x:pnat,v0:pnat,v1:leq(half(v0),double(v0))]==>v2:pnat=>leq(v2,s(s(s(v2)))),
  ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([],[leq1,equ(u(1),left)])]))then[elementary(istrue)]),step_case(ripple(direction_out,unblock_then_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),unblock(meta_ripple,unused,unused),unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[],[leq3,equ(u(1),left)],[])))then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v4))])]),lambda(v2,p_ind(v2,su(su(0,[leq1 of s(s(s(0)))],[v3]),[term_of(leq1)],[leq1]),[v3,v4,su(su(su(v4,[v5 of s(s(s(v3)))],[v6]),[leq3 of v3],[v5]),[term_of(leq3)],[leq3])])),
  [
  ]) ext _107372
 ]) ext _107845
]).
