| author | berghofe |
| Thu, 10 Oct 2002 14:19:17 +0200 | |
| changeset 13636 | fdf7e9388be7 |
| parent 13487 | 1291c6375c29 |
| permissions | -rw-r--r-- |
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(* Title : PRat.thy |
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ID : $Id$ |
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Author : Jacques D. Fleuriot |
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Copyright : 1998 University of Cambridge |
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Description : The positive rationals |
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*) |
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PRat = PNat + |
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constdefs |
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ratrel :: "((pnat * pnat) * (pnat * pnat)) set" |
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"ratrel == {p. ? x1 y1 x2 y2. p=((x1::pnat,y1),(x2,y2)) & x1*y2 = x2*y1}"
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typedef prat = "UNIV//ratrel" (quotient_def) |
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instance |
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prat :: {ord,plus,times}
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constdefs |
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7077
60b098bb8b8a
heavily revised by Jacques: coercions have alphabetic names;
paulson
parents:
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diff
changeset
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prat_of_pnat :: pnat => prat |
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"prat_of_pnat m == Abs_prat(ratrel``{(m,Abs_pnat 1)})"
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qinv :: prat => prat |
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"qinv(Q) == Abs_prat(UN (x,y):Rep_prat(Q). ratrel``{(y,x)})"
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defs |
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prat_add_def |
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7376
46f92a120af9
tidied, allowing pattern-matching in defs of prat_add and prat_mult
paulson
parents:
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diff
changeset
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"P + Q == Abs_prat(UN (x1,y1):Rep_prat(P). UN (x2,y2):Rep_prat(Q). |
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ratrel``{(x1*y2 + x2*y1, y1*y2)})"
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prat_mult_def |
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7376
46f92a120af9
tidied, allowing pattern-matching in defs of prat_add and prat_mult
paulson
parents:
7219
diff
changeset
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"P * Q == Abs_prat(UN (x1,y1):Rep_prat(P). UN (x2,y2):Rep_prat(Q). |
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ratrel``{(x1*x2, y1*y2)})"
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(*** Gleason p. 119 ***) |
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prat_less_def |
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"P < (Q::prat) == EX T. P + T = Q" |
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prat_le_def |
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"P <= (Q::prat) == ~(Q < P)" |
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end |
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