User:Boris Tsirelson/Sandbox1: Difference between revisions

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For a [[theory (mathematics)|mathematical theory]], correctness means formalizability.
For a [[theory (mathematics)|mathematical theory]], correctness means formalizability.
"In practice, the mathematician ... is content to bring the exposition to a point where his experience and mathematical flair tell him that translation into formal language would be no more than an exercise of patience (though doubtless a very tedious one)."<ref>{{harvnb|Bourbaki|1968|loc=page 8}}.</ref>


[http://www.cse.unsw.edu.au/~kleing/top100/#1 Top 100 theorems in Isabelle] +
[http://www.cse.unsw.edu.au/~kleing/top100/#1 Top 100 theorems in Isabelle] +
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{{Image|Isabelle15.png|right|350px|...and the theorems.}}
{{Image|Isabelle15.png|right|350px|...and the theorems.}}
==Notes==
{{reflist|2}}
==References==
{{Citation
| last = Bourbaki
| first = Nicolas
| title = Elements of mathematics: Theory of sets
| year = 1968
| publisher = Hermann (original), Addison-Wesley (translation)
}}.

Revision as of 06:21, 9 August 2010

For a mathematical theory, correctness means formalizability. "In practice, the mathematician ... is content to bring the exposition to a point where his experience and mathematical flair tell him that translation into formal language would be no more than an exercise of patience (though doubtless a very tedious one)."[1]


Top 100 theorems in Isabelle + Formalizing 100 Theorems + Isabelle + Download and installation + Projects + The Isabelle2009-2 Library + IsarMathLib: A library of formalized mathematics for Isabelle/ZF

(CC) Image: Boris Tsirelson
The graphical user interface started.




The graphical user interface started.



(CC) Image: Boris Tsirelson
The source file is read.



  The source file is read.

(CC) Image: Boris Tsirelson
Definitions are processed; the formulation of the first lemma is being processed.


Definitions are processed; the formulation of the first lemma is being processed.

(CC) Image: Boris Tsirelson
The formulation of the first lemma is processed; the goal is pending.

The formulation of the first lemma is processed; the goal is pending.

(CC) Image: Boris Tsirelson
At last, a really serious lemma.
(CC) Image: Boris Tsirelson
The goal.
(CC) Image: Boris Tsirelson
"We have", why?
(CC) Image: Boris Tsirelson
Here is why!
(CC) Image: Boris Tsirelson
Really complicated arguments...
(CC) Image: Boris Tsirelson
Happy end is coming.
(CC) Image: Boris Tsirelson
The theorem is proved.
(CC) Image: Boris Tsirelson
Some options of the Proof General.
(CC) Image: Boris Tsirelson
Isabelle, show us your methods...
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...and your term bindings...
(CC) Image: Boris Tsirelson
...and the theorems.

Notes

  1. Bourbaki 1968, page 8.

References

Bourbaki, Nicolas (1968), Elements of mathematics: Theory of sets, Hermann (original), Addison-Wesley (translation).