| author | paulson |
| Mon, 16 Aug 1999 18:41:32 +0200 | |
| changeset 7219 | 4e3f386c2e37 |
| parent 7077 | 60b098bb8b8a |
| child 7825 | 1be9b63e7d93 |
| permissions | -rw-r--r-- |
| 7219 | 1 |
(* Title : PReal.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 reals as Dedekind sections of positive |
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rationals. Fundamentals of Abstract Analysis [Gleason- p. 121] |
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provides some of the definitions. |
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*) |
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PReal = PRat + |
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typedef preal = "{A::prat set. {} < A & A < {q::prat. True} &
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(!y: A. ((!z. z < y --> z: A) & |
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(? u: A. y < u)))}" (preal_1) |
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instance |
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preal :: {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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preal_of_prat :: prat => preal |
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60b098bb8b8a
heavily revised by Jacques: coercions have alphabetic names;
paulson
parents:
5078
diff
changeset
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"preal_of_prat q == Abs_preal({x::prat. x < q})"
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pinv :: preal => preal |
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"pinv(R) == Abs_preal({w. ? y. w < y & qinv y ~: Rep_preal(R)})"
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psup :: preal set => preal |
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"psup(P) == Abs_preal({w. ? X: P. w: Rep_preal(X)})"
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defs |
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preal_add_def |
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"R + S == Abs_preal({w. ? x: Rep_preal(R). ? y: Rep_preal(S). w = x + y})"
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preal_mult_def |
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"R * S == Abs_preal({w. ? x: Rep_preal(R). ? y: Rep_preal(S). w = x * y})"
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preal_less_def |
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"R < (S::preal) == Rep_preal(R) < Rep_preal(S)" |
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preal_le_def |
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"R <= (S::preal) == Rep_preal(R) <= Rep_preal(S)" |
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end |
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