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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2017distributivity.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2017distributivity.tex" :end))
% (defun C () (interactive) (find-LATEXSH "lualatex 2017distributivity.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2017distributivity.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2017distributivity.pdf"))
% (defun e () (interactive) (find-LATEX "2017distributivity.tex"))
% (defun u () (interactive) (find-latex-upload-links "2017distributivity"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (defun d0 () (interactive) (find-ebuffer "2017distributivity.pdf"))
% (find-pdf-page "~/LATEX/2017distributivity.pdf")
% (find-sh0 "cp -v ~/LATEX/2017distributivity.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2017distributivity.pdf /tmp/pen/")
% file:///home/edrx/LATEX/2017distributivity.pdf
% file:///tmp/2017distributivity.pdf
% file:///tmp/pen/2017distributivity.pdf
% http://angg.twu.net/LATEX/2017distributivity.pdf
% (find-LATEX "2019.mk")
% (find-angg "LUA/distributivity.lua")
% (find-LATEXgrep "grep -nH -e istributi *.tex")
\documentclass[oneside]{book}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
%\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage{color} % (find-LATEX "edrx15.sty" "colors")
\usepackage{colorweb} % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
\usepackage{proof} % For derivation trees ("%:" lines)
\input diagxy % For 2D diagrams ("%D" lines)
\xyoption{curve} % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx15} % (find-angg "LATEX/edrx15.sty")
\input edrxaccents.tex % (find-angg "LATEX/edrxaccents.tex")
\input edrxchars.tex % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex % (find-dn4ex "edrxheadfoot.tex")
\input edrxgac2.tex % (find-LATEX "edrxgac2.tex")
%
\begin{document}
\catcode`\^^J=10
\directlua{dofile("dednat6load.lua")}
\directlua{dofile "edrxtikz.lua"} % (find-LATEX "edrxtikz.lua")
\directlua{dofile "edrxpict.lua"} % (find-LATEX "edrxpict.lua")
%L V.__tostring = function (v) return format("(%.3f,%.3f)", v[1], v[2]) end
% (fooi "->" "→" "|-" "⊢" "&" "∧")
%:*∧*\land *
%:*v*\lor *
This proof presents no problems:
(It uses ``ND with a single hypothesis'')
%:
%:
%: [P∧R]^1 [Q∧R]^1
%: ------- -------
%: P [P∧R]^1 Q [Q∧R]^1
%: --- ------- ---- ----
%: P∨Q R P∨Q R
%: ----------- -----------
%: (P∧R)∨(Q∧R) (P∨Q)∧R (P∨Q)∧R
%: ----------------------------------------
%: (P∨Q)∧R
%:
%: ^distr-ok-dn
%:
%: [P∧R]^1 [Q∧R]^1
%: ------- -------
%: P Q [P∧R]^1 [Q∧R]^1
%: --- ---- ------- -------
%: (P∧R)∨(Q∧R) P∨Q P∨Q (P∧R)∨(Q∧R) R R
%: -------------------------- -------------------------
%: (P∨Q) R
%: -------------------------------
%: (P∨Q)∧R
%:
%: ^distr-ok-dn2
%:
%: ------ ------
%: P∧Q⊢P P⊢PvQ
%: ------------- -------- ------ ------
%: P∧Q⊢PvQ Q∧R⊢PvQ P∧R⊢R Q∧R⊢R
%: --------------------- --------------
%: (P∧R)v(Q∧R)⊢PvQ (P∧R)v(Q∧R)⊢R
%: ------------------------------------
%: (P∧R)v(Q∧R)⊢(PvQ)∧R
%:
%: ^distr-ok-seq
%:
\pu
$$\ded{distr-ok-dn}$$
$$\ded{distr-ok-dn2}$$
$$\ded{distr-ok-seq}$$
%: P∧((PvQ)∧R)⊢P P∧((PvQ)∧R)⊢R Q∧((PvQ)∧R)⊢Q Q∧((PvQ)∧R)⊢R
%: ------------------------------ ------------------------------
%: P∧((PvQ)∧R)⊢P∧R Q∧((PvQ)∧R)⊢Q∧R
%: ------------------- ------------------
%: P⊢((PvQ)∧R)→(P∧R) Q⊢((PvQ)∧R)→(Q∧R)
%: -----------------------------------------------
%: (PvQ)∧R⊢PvQ PvQ⊢((PvQ)∧R)→(P∧R)
%: ======================= ------------------------
%: (PvQ)∧R⊢(PvQ)∧((PvQ)∧R) (PvQ)∧((PvQ)∧R)⊢P∧RvQ∧R
%: -----------------------------------------------
%: (PvQ)∧R⊢P∧RvQ∧R
%:
%: ^distr-ok-hard
%:
% $$\pu
% \ded{distr-ok-hard}
% $$
This one, which seems to require `$→$', fails in some way:
%:
%: (PvQ)∧R (PvQ)∧R
%: ------ -------
%: [P]^1 R [Q]^1 R
%: --------- ---------
%: P∧R Q∧R
%: ------------ -----------
%: (PvQ)∧R (P∧R)v(Q∧R) (P∧R)v(Q∧R)
%: ------- --------------------------
%: PvQ (P∧R)v(Q∧R)
%: ----------------1
%: (P∧R)v(Q∧R)
%:
%: ^distr-weird-1
%:
$$\pu
\ded{distr-weird-1}
$$
%:
%: P,(PvQ)∧R⊢P P,(PvQ)∧R⊢R Q,(PvQ)∧R⊢Q Q,(PvQ)∧R⊢R
%: -------------------------- --------------------------
%: P,(PvQ)∧R⊢P∧R Q,(PvQ)∧R⊢Q∧R
%: ================== ==================
%: P,(PvQ)∧R⊢P∧RvQ∧R Q,(PvQ)∧R⊢P∧RvQ∧R
%: ---------------------- ------------------
%: P⊢((PvQ)∧R)→(P∧RvQ∧R) Q⊢((PvQ)∧R)→(P∧RvQ∧R)
%: --------------------------------------------------
%: PvQ⊢((PvQ)∧R)→(P∧RvQ∧R)
%: ==========================
%: PvQ∧R⊢((PvQ)∧R)→(P∧RvQ∧R)
%:
%: ^distr-weird-2
%:
$$\pu
\ded{distr-weird-2}
$$
\newpage
% (find-books "__alg/__alg.el" "davey-priestley")
% (find-daveypriestleypage (+ 14 88) "The M3-N5 Theorem")
%L forths["-"] = function () pusharrow("-") end
%D diagram ??
%D 2Dx 100 +20 +20 +40
%D 2D 100 A0
%D 2D / \
%D 2D +20 A1 \
%D 2D / \ \
%D 2D +20 A2 A3 A4
%D 2D \ / /
%D 2D +20 A5 /
%D 2D \ /
%D 2D +20 A6
%D 2D
%D ren A0 ==> B_1{∨}B_2
%D ren A1 ==> ·
%D ren A2 A3 A4 ==> A B_1 B_2
%D ren A5 ==> A{∧}B_1
%D ren A6 ==> A{∧}B_2
%D
%D (( A0 A1 - A0 A4 -
%D A1 A2 - A1 A3 - A2 A5 - A3 A5 -
%D A4 A6 - A5 A6 -
%D
%D newnode: A2L at: @A2+v(-25,0) .TeX= A{∧}(\bigvee_{i}B_i)= place
%D newnode: A5L at: @A5+v(-45,0) .TeX= \bigvee_{i}(A{∧}B_i)= place
%D ))
%D enddiagram
%D
$$\pu
\diag{??}
$$
\GenericWarning{Success:}{Success!!!} % Used by `M-x cv'
\end{document}
% Local Variables:
% coding: utf-8-unix
% ee-tla: "dis"
% End: