proper congruence rule for image operator

--HG--
extra : rebase_source : 71f59936260619419f4d3f7f86d1b930bc771065

isabelle update -u control_cartouches;

A few new results, elimination of duplicates and more use of "pairwise"

standardized towards new-style formal comments: isabelle update_comments;

ran isabelle update_op on all sources

session-qualified theory imports: isabelle imports -U -i -d '~~/src/Benchmarks' -a;

eliminated old 'def';
tuned comments;

fix HOL-Probability-ex

isabelle update_cartouches -c -t;

tuned proofs -- less legacy;

tuned whitespace;

Hypsubst preserves equality hypotheses

Fixes included for various theories affected by this change.

--HG--
extra : rebase_source : b0150e06a14c2821e03208834282be6eca87aae0

fixed document generation for HOL-Probability

tuned proofs -- clarified flow of facts wrt. calculation;

reworked Probability theory

--HG--
extra : rebase_source : 04bef352ab6c7feafcf64ecca49fecffac43bb41

prefer abs_def over def_raw;

avoid undeclared variables in let bindings;
tuned proofs;

remove unnecessary sublocale instantiations in HOL-Probability (for clarity and speedup); remove Infinite_Product_Measure.product_prob_space which was a duplicate of Probability_Measure.product_prob_space

use list theorems in Dining Cryptographers and Koepf Duermuth Countermeasure

new fastforce replacing fastsimp - less confusing name

Rename extreal => ereal

--HG--
rename : src/HOL/Library/Extended_Reals.thy => src/HOL/Library/Extended_Real.thy

reworked Probability theory: measures are not type restricted to positive extended reals

the measure valuation is again part of the measure_space type, instead of an explicit parameter to the locale;
changed syntax for simple_function, simple_integral, positive_integral, integral and RN_deriv.
introduced binder variants for simple_integral, positive_integral and integral.

it is known as the extended reals, not the infinite reals

--HG--
rename : src/HOL/Probability/Positive_Infinite_Real.thy => src/HOL/Probability/Positive_Extended_Real.thy

Support product spaces on sigma finite measures.
Introduce the almost everywhere quantifier.
Introduce 'morphism' theorems for most constants.
Prove uniqueness of measures on cut stable generators.
Prove uniqueness of the Radon-Nikodym derivative.
Removed misleading suffix from borel_space and lebesgue_space.
Use product spaces to introduce Fubini on the Lebesgue integral.
Combine Euclidean_Lebesgue and Lebesgue_Measure.
Generalize theorems about mutual information and entropy to arbitrary probability spaces.
Remove simproc mult_log as it does not work with interpretations.
Introduce completion of measure spaces.
Change type of sigma.
Introduce dynkin systems.

--HG--
rename : src/HOL/Probability/Borel.thy => src/HOL/Probability/Borel_Space.thy

Updated proofs in Dining Cryptographers theory

Rewrite the Probability theory.

Introduced pinfreal as real numbers with infinity.
Use pinfreal as value for measures.
Introduces Lebesgue Measure based on the integral in Multivariate Analysis.
Proved Radon Nikodym for arbitrary sigma finite measure spaces.

--HG--
rename : src/HOL/Probability/Lebesgue.thy => src/HOL/Probability/Lebesgue_Integration.thy

Cleanup information theory

Added Information theory and Example: dining cryptographers