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TeXDict begin 1 0 bop Black Black Black Black 728 448
a FA(Barendregt's)46 b(V)-11 b(ariable)46 b(Con)l(v)l(en)l(tion)g(in)f
(Rule)1655 598 y(Inductions)886 886 y Fz(Christian)27
b(Urban)1480 856 y Fy(1)1517 886 y Fz(,)g(Stefan)h(Berghofer)2177
856 y Fy(1)2213 886 y Fz(,)g(and)f(Mic)n(hael)g(Norrish)3006
856 y Fy(2)1555 1029 y Fx(1)1628 1060 y Fw(TU)f(Munic)n(h,)f(German)n
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b Fw(;)13 b Fk(xs)7 b Fw(])p Black 864 w(\(14\))p Black
523 3328 a Fz(hold.)43 b(Since)f Fr(\045)h Fz(is)f(assumed)g(to)h(b)r
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y Fg(\001)1357 3950 y Fs(as)h Fz(;)14 b Fr(\031)1527
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b Fw(\()p Fn(d)p Fw(\))21 b Fn(distinct)p Fw(\()p Fk(cs)6
b Fw(\))170 b(\(16\))523 4526 y Fz(Suc)n(h)31 b Fs(cs)39
b Fz(alw)n(a)n(ys)29 b(exists:)i(the)h(\014rst)f(and)g(the)h(second)e
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4625 y(the)23 b(sc)n(hematic)e(terms)h Fs(ts)6 b Fz([)p
Fr(\031)1403 4634 y Fg(\001)1442 4625 y Fs(as)h Fz(;)14
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b Fz(stand)22 b(for)g(\014nitely)h(supp)r(orted)e(ob)5
b(jects;)523 4725 y(the)25 b(third)h(can)e(also)g(b)r(e)i(obtained)e
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Fr(C)31 b Fz(is)523 4825 y(\014nitely)25 b(supp)r(orted;)f(the)g(last)g
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Fs(cs)31 b Fz(one)24 b(after)g(another)523 4924 y(a)n(v)n(oiding)i(the)
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1194 y Fk(xs)7 b Fw(]\)\))333 b(\(18\))523 1349 y Fz(hold.)27
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(can)g(infer)g(from)h(\(14\))f(and)g(the)h(equiv)-5 b(ari-)523
1440 y(ance)27 b(of)h(the)g(side-conditions)e(that)1227
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Fk(xs)7 b Fw(])568 b(\(19\))523 1750 y Fz(hold)31 b(\(w)n(e)g(use)f
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1750 y Fz(@)p Fr(\031)1884 1759 y Fg(\001)1922 1750 y
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2489 y Fk(xs)7 b Fw(])741 b(\(21\))523 2652 y Fz(Substituting)28
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4401 y(side-condition,)27 b Fr(x)c Fz(#)h Fr(\000)12
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y(principle)d(with)h Fr(\000)1106 1980 y Fj(0)1151 2011
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b Fw(=)21 b Fn(\000)317 b(M)30 b Fw(=)21 b Fn(M)316 b(T)31
b Fw(=)21 b Fn(T)523 2499 y Fz(whic)n(h)h(after)g(some)f(b)r(eta-con)n
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Fr(\000)1963 2884 y Fj(00)2028 2914 y Fp(`)g Fr(M)2183
2926 y Fy(1)2243 2914 y Fz(:)g Fr(T)2338 2926 y Fy(1)2398
2914 y Fp(!)g Fr(T)2553 2926 y Fy(2)2589 2914 y Fz(\))h
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2983 y Fj(00)2028 3013 y Fp(`)g Fr(M)2183 3025 y Fy(2)2243
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Fr(\000)1787 3083 y Fj(0)1833 3113 y Fp(`)23 b Fs(app)7
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r(out)g(the)h(relationship)f(b)r(et)n(w)n(een)g Fr(x)h
Fz(and)523 4526 y Fr(\000)586 4496 y Fj(0)609 4526 y
Fz(,)f(forcing)f(the)h(pro)n(v)n(er)d(to)j Fr(\013)p
Fz(-con)n(v)n(ert)e Fs(lam)7 b Fz(\()p Fr(x:M)i Fz(\))25
b(to)g(a)f(form)g(with)i(a)e(new)h(and)f(suitably)523
4625 y(fresh)j(b)r(ound)h(v)-5 b(ariable,)26 b Fs(lam)7
b Fz(\()p Fr(z)t(:)p Fz(\(\()p Fr(z)18 b(x)p Fz(\))1750
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b(.)27 b(A)n(t)h(this)f(p)r(oin)n(t,)h(the)g(simplicit)n(y)f(of)h(the)
523 4725 y(pro)r(of)23 b(using)g(the)g(v)-5 b(ariable)22
b(con)n(v)n(en)n(tion)g(disapp)r(ears:)g(the)i(inductiv)n(e)f(h)n(yp)r
(othesis)g(is)g(m)n(uc)n(h)523 4825 y(harder)36 b(to)i(sho)n(w)f
(applicable)g(b)r(ecause)g(it)h(men)n(tions)f Fr(M)9
b Fz(,)38 b(but)g(the)g(desired)f(goal)f(is)i(in)523
4924 y(terms)27 b(of)h(\()p Fr(z)17 b(x)p Fz(\))1016
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eop end
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1704 y Fx(2)2131 1696 y Fv(b)n(y)g Fk(auto)552 1787 y
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1795 y Fx(1)1481 1787 y Fw(and)e(T)n(yp)r(e)1803 1795
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h(straigh)n(tforw)n(ard)d(v)n(c-compatible)523 3494 y
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y Fg(\001)2467 3688 y Fn(N)8 b Fw(\)])p Black 681 w(\(23\))p
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Fw(\))g Fm([)g Fc(supp)q Fw(\()p Fn(N)8 b Fw(\))p Black
515 w(\(24\))p Black 648 4017 a Fz(With)21 b(this)g(w)n(e)g(can)f
(start)h(to)g(c)n(hec)n(k)f(the)h(v)n(c-compatibilit)n(y)f(conditions:)
g(the)h(condition)523 4117 y(ab)r(out)d(equiv)-5 b(ariance)18
b(of)g(functions)h(and)f(side-conditions)g(is)g(again)f(easily)h
(con\014rmed.)g(The)523 4216 y(second)28 b(condition)g(is)g(that)g(b)r
(ound)h(v)-5 b(ariables)27 b(are)g(free)h(in)g(the)h(relation's)e
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b(and)f Fr(y)j Fz(#)e Fs(lam)7 b Fz(\()p Fr(y)s(:M)3350
4286 y Fj(0)3373 4316 y Fz(\))523 4416 y(hold.)36 b(A)g(problem)g
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4428 y Fy(4)2334 4416 y Fz(.)h(Here)e(w)n(e)h(ha)n(v)n(e)f(to)h(sho)n
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