problem([]==>x:int=>a:int list=>b:int list=>member(x,a)=>member(x,union(a,b)),
ind_strat(induction(lemma(list_primitive)-[(a:int list)-v1::v0])then[base_case(sym_eval(normalize_term([reduction([1],[member1,equ(u(1),left)]),reduction([2,2],[union1,equ(int list,left)])]))then[elementary(intro(new[x])then[intro(new[b])then[intro(new[v0])then[elim(v0),wfftacs],wfftacs],wfftacs])]),step_case(ripple(direction_out,casesplit(disjunction([member(v1,b)=>void,member(v1,b)]))then[wave(direction_out,[2,2],[union4,equ(int list,left)],[])then[casesplit(disjunction([x=v1 in int=>void,x=v1 in int]))then[wave(direction_out,[2],[member3,equ(u(1),left)],[])then[wave(direction_out,[1],[member3,equ(u(1),left)],[])],wave(direction_out,[2],[member2,complementary,equ(u(1),left)],[])]],wave(direction_out,[2,2],[union3,equ(int list,left)],[])then[casesplit(disjunction([x=v1 in int=>void,x=v1 in int]))then[wave(direction_out,[1],[member3,equ(u(1),left)],[]),wave(direction_out,[1],[member2,complementary,equ(u(1),left)],[])]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2)),idtac,unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v2)),idtac])]),lambda(v0,lambda(v1,lambda(v2,lambda(v3,su(su(su(v6,[v5 of v2],[v6]),[v4 of v0],[v5]),[v3 of v1],[v4]))of lambda(a,list_ind(a,lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(x,lambda(b,lambda(v0,any(v0)))),[union1 of v1],[v2]),[term_of(union1)],[union1]))),[member1 of v0],[v2]),[term_of(member1)],[member1]))),[v1,v0,v2,lambda(v3,lambda(v4,lambda(v5,su(su(v7,[v6 of v3],[v7]),[v5 of v4],[v6]))of lambda(b,lambda(v4,decide(v4,[v5,lambda(v3,lambda(v4,su(su(su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(x,lambda(v5,decide(v5,[v6,lambda(v4,su(su(su(su(su(su(su(su(su(su(su(su(v6,[v5 of b],[v6]),[v2 of x],[v5]),[v7 of v4],[v5]),[v6 of v0],[v7]),[v5 of v1],[v6]),[member3 of x],[v5]),[term_of(member3)],[member3]),[v7 of v4],[v5]),[v6 of union(v0,b)],[v7]),[v5 of v1],[v6]),[member3 of x],[v5]),[term_of(member3)],[member3]))of v6],[v7,lambda(v4,su(su(su(su(su(_66136,[v7 of v4],[v5]),[v6 of union(v0,b)],[v7]),[v5 of v1],[v6]),[member2 of x],[v5]),[term_of(member2)],[member2]))of v7]))of su(su(su(v6,[v5 of v1],[v6]),[v4 of x],[v5]),[term_of(deceqint)],[v4])),[v7 of v3],[v5]),[v6 of b],[v7]),[v5 of v0],[v6]),[union4 of v1],[v5]),[term_of(union4)],[union4])))of v5],[v6,lambda(v3,lambda(v4,su(su(su(su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(x,lambda(v5,decide(v5,[v6,lambda(v4,su(su(su(su(su(su(su(v6,[v5 of b],[v6]),[v2 of x],[v5]),[v7 of v4],[v5]),[v6 of v0],[v7]),[v5 of v1],[v6]),[member3 of x],[v5]),[term_of(member3)],[member3]))of v6],[v7,lambda(v4,su(su(su(su(su(_65854,[v7 of v4],[v5]),[v6 of v0],[v7]),[v5 of v1],[v6]),[member2 of x],[v5]),[term_of(member2)],[member2]))of v7]))of su(su(su(v6,[v5 of v1],[v6]),[v4 of x],[v5]),[term_of(deceqint)],[v4])),[v7 of v3],[v5]),[v6 of b],[v7]),[v5 of v0],[v6]),[union3 of v1],[v5]),[term_of(union3)],[union3])))of v6]))of su(su(su(v5,[v4 of b],[v5]),[v3 of v1],[v4]),[term_of(decmember)],[v3]))))]))))),
[problem([a:int list,v1:int,v0:int list,v2:x:int=>b:int list=>member(x,v0)=>member(x,union(v0,b)),b:int list,v3:member(v1,b)=>void,x:int,v4:x=v1 in int]==>member(x,v1::v0)=>{true},
 elementary(intro(new[v5])then[istrue,wfftacs]),lambda(v5,0),
 [
 ]) ext _66136,
 problem([a:int list,v1:int,v0:int list,v2:x:int=>b:int list=>member(x,v0)=>member(x,union(v0,b)),b:int list,v3:member(v1,b),x:int,v4:x=v1 in int]==>{true}=>member(x,union(v0,b)),
 sym_eval(equal(v4,right)),_65588,
 [problem([a:int list,v1:int,v0:int list,v2:x:int=>b:int list=>member(x,v0)=>member(x,union(v0,b)),b:int list,v3:member(v1,b),x:int]==>{true}=>member(v1,union(v0,b)),
  ind_strat(induction(lemma(list_primitive)-[(v0:int list)-v5::v4])then[base_case(sym_eval(normalize_term([reduction([2,2],[union1,equ(int list,left)])]))then[elementary(intro(new[v4])then[hyp(v3),wfftacs])]),step_case(ripple(direction_out,casesplit(disjunction([member(v5,b)=>void,member(v5,b)]))then[wave(direction_out,[2,2],[union4,equ(int list,left)],[])then[casesplit(disjunction([v1=v5 in int=>void,v1=v5 in int]))then[wave(direction_out,[2],[member3,equ(u(1),left)],[]),wave(direction_out,[2],[member2,complementary,equ(u(1),left)],[])]],wave(direction_out,[2,2],[union3,equ(int list,left)],[])])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v6)),idtac,unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v6))])]),list_ind(v0,su(su(lambda(v4,v3),[union1 of b],[v4]),[term_of(union1)],[union1]),[v5,v4,v6,lambda(v8,decide(v8,[v9,lambda(v7,su(su(su(su(su(lambda(v9,decide(v9,[v10,lambda(v8,su(su(su(su(su(v6,[v11 of v8],[v9]),[v10 of union(v4,b)],[v11]),[v9 of v5],[v10]),[member3 of v1],[v9]),[term_of(member3)],[member3]))of v10],[v11,lambda(v8,su(su(su(su(su(_64965,[v11 of v8],[v9]),[v10 of union(v4,b)],[v11]),[v9 of v5],[v10]),[member2 of v1],[v9]),[term_of(member2)],[member2]))of v11]))of su(su(su(v10,[v9 of v5],[v10]),[v8 of v1],[v9]),[term_of(deceqint)],[v8]),[v10 of v7],[v8]),[v9 of b],[v10]),[v8 of v4],[v9]),[union4 of v5],[v8]),[term_of(union4)],[union4]))of v9],[v10,lambda(v7,su(su(su(su(su(v6,[v10 of v7],[v8]),[v9 of b],[v10]),[v8 of v4],[v9]),[union3 of v5],[v8]),[term_of(union3)],[union3]))of v10]))of su(su(su(v9,[v8 of b],[v9]),[v7 of v5],[v8]),[term_of(decmember)],[v7])]),
  [problem([a:int list,v1:int,v0:int list,v2:x:int=>b:int list=>member(x,v0)=>member(x,union(v0,b)),b:int list,v3:member(v1,b),x:int,v5:int,v4:int list,v6:{true}=>member(v1,union(v4,b)),v7:member(v5,b)=>void,v8:v1=v5 in int]==>{true}=>{true},
   elementary(intro(new[v9])then[hyp(v9),wfftacs]),lambda(v9,v9),
   [
   ]) ext _64965
  ]) ext _65588
 ]) ext _65854
]).
