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1	Minimal·Logic·for·Computable·Functionals	1	Minimal·Logic·for·Computable·Functionals
2	Helmut·Schwichtenberg	2	Helmut·Schwichtenberg

3	Mathematisches·Institut·der·Universität·München	3	Mathematisches·Institut·der·Universität·München
4	June·6,·2020	4	June·7,·2020

5	\xcContents	5	\xcContents
6	Chapter·1.·Minimal·Logic	6	Chapter·1.·Minimal·Logic
7	1.1.·Natural·Deduction	7	1.1.·Natural·Deduction
8	1.2.·Embedding·Classical·and·Intuitionistic·Logic	8	1.2.·Embedding·Classical·and·Intuitionistic·Logic
9	1.3.·Glivenko’s·Theorem	9	1.3.·Glivenko’s·Theorem
10	1.4.·Negative·Translation	10	1.4.·Negative·Translation


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1	The·Minlog·Proof·Checker:·Mpc	1	The·Minlog·Proof·Checker:·Mpc
2	Martin·Ruckert	2	Martin·Ruckert
3	June·6,·2020	3	June·7,·2020

4	Contents	4	Contents
5	1·Lexical·Structure	5	1·Lexical·Structure

6	2	6	2

7	2·Syntax	7	2·Syntax


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226	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/examples/warshall/	226	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/examples/warshall/
227	-rw-r--r--···0·root·········(0)·root·········(0)······651·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/Makefile	227	-rw-r--r--···0·root·········(0)·root·········(0)······651·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/Makefile
228	-rw-r--r--···0·root·········(0)·root·········(0)·····2548·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/lemmas.mpc	228	-rw-r--r--···0·root·········(0)·root·········(0)·····2548·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/lemmas.mpc
229	-rw-r--r--···0·root·········(0)·root·········(0)····13888·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/warshall.mpc	229	-rw-r--r--···0·root·········(0)·root·········(0)····13888·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/warshall.mpc
230	-rw-r--r--···0·root·········(0)·root·········(0)····61021·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/warshall.save	230	-rw-r--r--···0·root·········(0)·root·········(0)····61021·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/warshall.save
231	-rw-r--r--···0·root·········(0)·root·········(0)·····8000·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/warshall.scm	231	-rw-r--r--···0·root·········(0)·root·········(0)·····8000·2010-02-20·23:51:35.000000·./usr/share/doc/minlog/examples/warshall/warshall.scm
232	-rw-r--r--···0·root·········(0)·root·········(0)···754148·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/mlcf.pdf	232	-rw-r--r--···0·root·········(0)·root·········(0)···754148·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/mlcf.pdf
233	-rw-r--r--···0·root·········(0)·root·········(0)···188~~724~~·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/mpcref.pdf	233	-rw-r--r--···0·root·········(0)·root·········(0)···188669·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/mpcref.pdf
234	-rw-r--r--···0·root·········(0)·root·········(0)···521146·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/ref.pdf	234	-rw-r--r--···0·root·········(0)·root·········(0)···521144·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/ref.pdf
235	-rw-r--r--···0·root·········(0)·root·········(0)···193983·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/reflection_manual.pdf	235	-rw-r--r--···0·root·········(0)·root·········(0)···193983·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/reflection_manual.pdf
236	-rw-r--r--···0·root·········(0)·root·········(0)···283003·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/tutor.pdf	236	-rw-r--r--···0·root·········(0)·root·········(0)···283003·2016-12-10·01:03:58.000000·./usr/share/doc/minlog/tutor.pdf
237	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/doc-base/	237	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/doc-base/
238	-rw-r--r--···0·root·········(0)·root·········(0)······462·2010-07-17·15:56:14.000000·./usr/share/doc-base/minlog	238	-rw-r--r--···0·root·········(0)·root·········(0)······462·2010-07-17·15:56:14.000000·./usr/share/doc-base/minlog
239	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/emacs/	239	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/emacs/
240	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/emacs/site-lisp/	240	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/emacs/site-lisp/
241	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/emacs/site-lisp/minlog/	241	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2016-12-10·01:03:58.000000·./usr/share/emacs/site-lisp/minlog/


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36	9.3.·Substitution	36	9.3.·Substitution
37	9.4.·Display	37	9.4.·Display
38	9.5.·Classical·logic	38	9.5.·Classical·logic
39	10.·Interactive·theorem·proving·with·partial·proofs	39	10.·Interactive·theorem·proving·with·partial·proofs
40	10.1.·Partial·proofs	40	10.1.·Partial·proofs
41	10.2.·Interactive·theorem·proving	41	10.2.·Interactive·theorem·proving
42	11.·Search	42	11.·Search
43	Date:·June·6,·2020.	43	Date:·June·7,·2020.
44	1	44	1

45	2	45	2
46	2	46	2
47	3	47	3
48	3	48	3
49	4	49	4