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4 <H2>Real--Dedekind Cut Construction of the Real Line</H2> |
4 <H2>Real--Dedekind Cut Construction of the Real Line</H2> |
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6 <P>Requires <A HREF="../Integ/Equiv.thy">Equiv.thy</A> in the subdirectory <A |
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7 HREF="../Integ">HOL/Integ</A>. |
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9 <UL> |
6 <UL> |
10 <LI><A HREF="PNat.thy">PNat</A> The positive integers (very much the same as <A HREF="../Nat.thy">Nat.thy</A>!) |
7 <LI><A HREF="PNat.html">PNat</A> The positive integers (very much the same as <A HREF="../Nat.html">Nat.thy</A>!) |
11 <LI><A HREF="PRat.thy">PRat</A> The positive rationals |
8 <LI><A HREF="PRat.html">PRat</A> The positive rationals |
12 <LI><A HREF="PReal.thy">PReal</A> The positive reals constructed using Dedekind cuts |
9 <LI><A HREF="PReal.html">PReal</A> The positive reals constructed using Dedekind cuts |
13 <LI><A HREF="Real.thy">Real</A> The real numbers |
10 <LI><A HREF="Real.html">Real</A> The real numbers |
14 <LI><A HREF="Lubs.thy">Lubs</A> Definition of upper bounds, lubs and so on. |
11 <LI><A HREF="Lubs.html">Lubs</A> Definition of upper bounds, lubs and so on. |
15 (Useful e.g. in Fleuriot's NSA theory) |
12 (Useful e.g. in Fleuriot's NSA theory) |
16 <LI><A HREF="RComplete.thy">RComplete</A> Proof of completeness of reals in form of the supremum |
13 <LI><A HREF="RComplete.html">RComplete</A> Proof of completeness of reals in form of the supremum |
17 property. Also proofs that the reals have the Archimedean |
14 property. Also proofs that the reals have the Archimedean |
18 property. |
15 property. |
19 <LI><A HREF="RealAbs.thy">RealAbs</A> The absolute value function defined for the reals |
16 <LI><A HREF="RealAbs.html">RealAbs</A> The absolute value function defined for the reals |
20 </UL> |
17 </UL> |
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22 <P>Last modified on $Date$ |
19 <P>Last modified on $Date$ |
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