| author | wenzelm |
| Tue, 24 Aug 1999 11:50:58 +0200 | |
| changeset 7333 | 6cb15c6f1d9f |
| parent 7219 | 4e3f386c2e37 |
| child 7376 | 46f92a120af9 |
| permissions | -rw-r--r-- |
| 5078 | 1 |
(* 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 + Equiv + |
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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 = "{x::(pnat*pnat).True}/ratrel" (Equiv.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:
5078
diff
changeset
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prat_of_pnat :: pnat => prat |
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60b098bb8b8a
heavily revised by Jacques: coercions have alphabetic names;
paulson
parents:
5078
diff
changeset
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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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7077
60b098bb8b8a
heavily revised by Jacques: coercions have alphabetic names;
paulson
parents:
5078
diff
changeset
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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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"P + Q == Abs_prat(UN p1:Rep_prat(P). UN p2:Rep_prat(Q). |
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split(%x1 y1. split(%x2 y2. ratrel^^{(x1*y2 + x2*y1, y1*y2)}) p2) p1)"
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prat_mult_def |
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"P * Q == Abs_prat(UN p1:Rep_prat(P). UN p2:Rep_prat(Q). |
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split(%x1 y1. split(%x2 y2. ratrel^^{(x1*x2, y1*y2)}) p2) p1)"
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(*** Gleason p. 119 ***) |
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prat_less_def |
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"P < (Q::prat) == ? 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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