problem([]==>x:int=>y:int list=>ordered(x::y)=>ordered(y),
ind_strat(induction(lemma(list_ind)-[(y:int list)-v0::v2::v1])then[base_case(sym_eval(normalize_term([reduction([1],[ordered2,equ(u(1),left)]),reduction([2],[ordered1,equ(u(1),left)])]))then[elementary(intro(new[x])then[intro(new[v0])then[hyp(v0),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([2],[ordered2,equ(u(1),left)])])then[casesplit(disjunction([v0<x=>void,v0<x]))then[normalize_term([reduction([1],[ordered4,equ(u(1),left)]),reduction([1],[ordered2,equ(u(1),left)])]),normalize_term([reduction([1],[ordered3,equ(u(1),left)])])]])then[elementary(intro(new[v2])then[hyp(v2),wfftacs]),elementary(intro(new[v2])then[istrue,wfftacs])]),step_case(ripple(direction_out,casesplit(disjunction([v2<v0=>void,v2<v0]))then[wave(direction_out,[2],[ordered4,equ(u(1),left)],[])then[casesplit(disjunction([v0<x=>void,v0<x]))then[wave(direction_out,[1],[ordered4,equ(u(1),left)],[]),wave(direction_out,[1],[ordered3,complementary,equ(u(1),left)],[])]],wave(direction_out,[2],[ordered3,complementary,equ(u(1),left)],[])then[casesplit(disjunction([v0<x=>void,v0<x]))then[idtac,idtac]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v3)),idtac,idtac,idtac])]),lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(y,su(lambda(v5,su(su(su(su(su(su(v0,[v10 of y],[v0]),[v9 of lambda(v0,lambda(v2,lambda(v1,lambda(v3,lambda(v5,decide(v5,[v6,lambda(v4,lambda(v5,su(su(su(su(su(lambda(v6,su(v7,[v6 of v5],[v7]))of lambda(x,lambda(v6,decide(v6,[v7,lambda(v5,su(su(su(su(su(su(v6,[v3 of v0],[v6]),[v8 of v5],[v6]),[v7 of(v2::v1)],[v8]),[v6 of v0],[v7]),[ordered4 of x],[v6]),[term_of(ordered4)],[ordered4]))of v7],[v8,lambda(v5,su(su(su(su(su(_108822,[v8 of v5],[v6]),[v7 of(v2::v1)],[v8]),[v6 of v0],[v7]),[ordered3 of x],[v6]),[term_of(ordered3)],[ordered3]))of v8]))of su(su(su(v7,[v6 of x],[v7]),[v5 of v0],[v6]),[term_of(decless2)],[v5])),[v8 of v4],[v6]),[v7 of v1],[v8]),[v6 of v2],[v7]),[ordered4 of v0],[v6]),[term_of(ordered4)],[ordered4])))of v6],[v7,lambda(v4,lambda(v5,su(su(su(su(su(lambda(v6,su(v7,[v6 of v5],[v7]))of lambda(x,lambda(v6,decide(v6,[v7,lambda(v5,_108647)of v7],[v8,lambda(v5,_108637)of v8]))of su(su(su(v7,[v6 of x],[v7]),[v5 of v0],[v6]),[term_of(decless2)],[v5])),[v8 of v4],[v6]),[v7 of v1],[v8]),[v6 of v2],[v7]),[ordered3 of v0],[v6]),[term_of(ordered3)],[ordered3])))of v7]))of su(su(su(v6,[v5 of v0],[v6]),[v4 of v2],[v5]),[term_of(decless2)],[v4])))))],[v10]),[v8 of lambda(v0,lambda(v1,su(su(lambda(v2,su(v3,[v2 of v1],[v3]))of lambda(x,lambda(v2,decide(v2,[v3,lambda(v1,su(su(su(su(su(su(su(lambda(v2,v2),[ordered2 of v0],[v2]),[term_of(ordered2)],[ordered2]),[v4 of v1],[v2]),[v3 of nil],[v4]),[v2 of v0],[v3]),[ordered4 of x],[v2]),[term_of(ordered4)],[ordered4]))of v3],[v4,lambda(v1,su(su(su(su(su(lambda(v2,0),[v4 of v1],[v2]),[v3 of nil],[v4]),[v2 of v0],[v3]),[ordered3 of x],[v2]),[term_of(ordered3)],[ordered3]))of v4]))of su(su(su(v3,[v2 of x],[v3]),[v1 of v0],[v2]),[term_of(decless2)],[v1])),[ordered2 of v0],[v2]),[term_of(ordered2)],[ordered2])))],[v9]),[v7 of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(x,lambda(v0,v0)),[term_of(ordered1)],[ordered1])),[ordered2 of v0],[v1]),[term_of(ordered2)],[ordered2]))],[v8]),[v6 of lambda(y,x:int=>ordered(x::y)=>ordered(y))],[v7]),[v5 of int],[v6]))of v4,[term_of(list_ind)],[v4])))),
[problem([y:int list,v0:int,v2:int,v1:int list,v3:x:int=>ordered(x::v2::v1)=>ordered(v2::v1),v4:v2<v0=>void,x:int,v5:v0<x]==>void=>ordered(v2::v1),
 elementary(intro(new[v6])then[elim(v6),wfftacs]),lambda(v6,any(v6)),
 [
 ]) ext _108822,
 problem([y:int list,v0:int,v2:int,v1:int list,v3:x:int=>ordered(x::v2::v1)=>ordered(v2::v1),v4:v2<v0,x:int,v5:v0<x=>void]==>ordered(x::v0::v2::v1)=>void,
 sym_eval(normalize_term([reduction([1],[ordered4,equ(u(1),left)]),reduction([1],[ordered3,equ(u(1),left)])]))then[elementary(intro(new[v6])then[hyp(v6),wfftacs])],su(su(su(su(su(su(su(su(su(su(lambda(v6,v6),[v8 of v4],[v6]),[v7 of v1],[v8]),[v6 of v2],[v7]),[ordered3 of v0],[v6]),[term_of(ordered3)],[ordered3]),[v8 of v5],[v6]),[v7 of(v2::v1)],[v8]),[v6 of v0],[v7]),[ordered4 of x],[v6]),[term_of(ordered4)],[ordered4]),
 [
 ]) ext _108647,
 problem([y:int list,v0:int,v2:int,v1:int list,v3:x:int=>ordered(x::v2::v1)=>ordered(v2::v1),v4:v2<v0,x:int,v5:v0<x]==>ordered(x::v0::v2::v1)=>void,
 sym_eval(normalize_term([reduction([1],[ordered3,equ(u(1),left)])]))then[elementary(intro(new[v6])then[hyp(v6),wfftacs])],su(su(su(su(su(lambda(v6,v6),[v8 of v5],[v6]),[v7 of(v2::v1)],[v8]),[v6 of v0],[v7]),[ordered3 of x],[v6]),[term_of(ordered3)],[ordered3]),
 [
 ]) ext _108637
]).
