LLWiki LaTeX Style

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(→‎Mathematical notations: \biorth and \triorth added)
m (→‎Proof trees: typo)
 
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| <math>A\limp B</math>
  
| <math>A\limp B</math>
 
| <pre>A\limp B</pre>
  
| <pre>A\limp B</pre>
  +
|-
  +
| <math>A\nlimp B</math>
  +
| <pre>A\nlimp B</pre>
  +
|-
  +
| <math>A\limpinv B</math>
  +
| <pre>A\limpinv B</pre>
  +
|-
  +
| <math>A\nlimpinv B</math>
  +
| <pre>A\nlimpinv B</pre>
 
|-
  
|-
 
| <math>A\linequiv B</math>
  
| <math>A\linequiv B</math>
 
| <pre>A\linequiv B</pre>
  
| <pre>A\linequiv B</pre>
  +
|-
  +
| <math>A\nlinequiv B</math>
  +
| <pre>A\nlinequiv B</pre>
 
|-
  
|-
 
| <math>\shpos A</math>
  
| <math>\shpos A</math>
Line 87: Line 99:
 
| <pre>\set{x}{P}</pre>
  
| <pre>\set{x}{P}</pre>
 
|-
  
|-
  +
| <math>\powerset{A}</math>
  +
| <pre>\powerset{A}</pre>
  +
|-
  +
| <math>\finpowerset{A}</math>
  +
| <pre>\finpowerset{A}</pre>
  +
|-
  +
| <math>\mulset{A}</math>
  +
| <pre>\mulset{A}</pre>
  +
|-
  +
| <math>\finmulset{A}</math>
  +
| <pre>\finmulset{A}</pre>
  +
|-
  +
| <math>\Bot</math>
  +
| <pre>\Bot</pre>
  +
|-
  +
| <math>A\Perp B</math>
  +
| <pre>A\Perp B</pre>
  +
|-
  +
| <math>A\pinj B</math>
  +
| <pre>A\pinj B</pre>
  +
|-
  +
| <math>\inner{A}{B}</math>
  +
| <pre>\inner{A}{B}</pre>
  +
|-
  +
| <math>\Inner{A}{B}</math>
  +
| <pre>\Inner{A}{B}</pre>
  +
|-
  +
|}
  +
  +
== Proof trees ==
  +
  +
Proof trees are described using a postfix syntax and terminated with <tt>\DisplayProof</tt>
  +
  +
{| border="1" cellpadding="10" cellspacing="0"
  +
|-
  +
| '''Description'''
  +
| '''Command'''
  +
| '''Example'''
  +
| '''LaTeX source'''
  +
|-
  +
| Axiom node <br /> (for hypotheses)
  +
| <pre>\AxRule</pre>
  +
| <math>
  +
\AxRule{\vdash A}
  +
\DisplayProof</math>
  +
| <pre>
  +
\AxRule{\vdash A}
  +
\DisplayProof</pre>
  +
|-
  +
| Nullary rule <br /> (for logical axioms)
  +
| <pre>\NulRule</pre>
  +
| <math>
  +
\NulRule{A \vdash A}
  +
\DisplayProof</math>
  +
| <pre>
  +
\NulRule{A \vdash A}
  +
\DisplayProof</pre>
  +
|-
  +
| Unary rule
  +
| <pre>\UnaRule</pre>
  +
| <math>
  +
\AxRule{\vdash \wn\Gamma, A}
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\UnaRule{\vdash \wn\Gamma, \oc A}
  +
\DisplayProof</math>
  +
| <pre>
  +
\AxRule{\vdash \wn\Gamma, A}
  +
\UnaRule{\vdash \wn\Gamma, \oc A}
  +
\DisplayProof</pre>
  +
|-
  +
| Binary rule
  +
| <pre>\BinRule</pre>
  +
| <math>
  +
\AxRule{\Gamma\vdash A}
  +
\AxRule{\Delta,A\vdash C}
  +
\BinRule{\Gamma,\Delta\vdash C}
  +
\DisplayProof</math>
  +
| <pre>
  +
\AxRule{\Gamma\vdash A}
  +
\AxRule{\Delta,A\vdash C}
  +
\BinRule{\Gamma,\Delta\vdash C}
  +
\DisplayProof</pre>
  +
|-
  +
| Ternary rule
  +
| <pre>\TriRule</pre>
  +
| <math>
  +
\AxRule{\vdash A}
  +
\AxRule{\vdash B}
  +
\AxRule{\vdash C}
  +
\TriRule{\vdash A\land B\land C}
  +
\DisplayProof</math>
  +
| <pre>
  +
\AxRule{\vdash A}
  +
\AxRule{\vdash B}
  +
\AxRule{\vdash C}
  +
\TriRule{\vdash A\land B\land C}
  +
\DisplayProof</pre>
  +
|-
  +
| Label <br /> (before any of the above)
  +
| <pre>\LabelRule</pre>
  +
| <math>\AxRule{\Gamma\vdash A}
  +
\AxRule{\Delta,A\vdash C}
  +
\LabelRule{\rulename{cut}}
  +
\BinRule{\Gamma,\Delta\vdash C}
  +
\DisplayProof</math>
  +
| <pre>
  +
\AxRule{\Gamma\vdash A}
  +
\AxRule{\Delta,A\vdash C}
  +
\LabelRule{\rulename{cut}}
  +
\BinRule{\Gamma,\Delta\vdash C}
  +
\DisplayProof</pre>
  +
|-
  +
| Proof ellipsis<br /> ''(two arguments !)''
  +
| <pre>\VdotsRule</pre>
  +
| <math>
  +
\AxRule{[A]}
  +
\VdotsRule{\pi}{B}
  +
\UnaRule{A\imp B}
  +
\DisplayProof</math>
  +
| <pre>
  +
\AxRule{[A]}
  +
\VdotsRule{\pi}{B}
  +
\UnaRule{A\imp B}
  +
\DisplayProof</pre>
 
|}
  
|}

Latest revision as of 14:51, 27 June 2013

[edit] Mathematical notations

A\orth 
A\orth
A\biorth 
A\biorth
A\triorth 
A\triorth
A\tens B 
A\tens B
A\parr B 
A\parr B
A\plus B 
A\plus B
A\with B 
A\with B
\one 
\one
\bot 
\bot
\zero 
\zero
\top 
\top
\oc A 
\oc A
\wn A 
\wn A
A\limp B 
A\limp B
A\nlimp B 
A\nlimp B
A\limpinv B 
A\limpinv B
A\nlimpinv B 
A\nlimpinv B
A\linequiv B 
A\linequiv B
A\nlinequiv B 
A\nlinequiv B
\shpos A 
\shpos A
\shneg A 
\shneg A
\shift A 
\shift A
\pg A 
\pg A
A\imp B 
A\imp B
\sem{A} 
\sem{A}
\web{A} 
\web{A}
A\coh B 
A\coh B
A\scoh B 
A\scoh B
A\incoh B 
A\incoh B
A\sincoh B 
A\sincoh B
A\cliq B 
A\cliq B
\set{x}{P} 
\set{x}{P}
\powerset{A} 
\powerset{A}
\finpowerset{A} 
\finpowerset{A}
\mulset{A} 
\mulset{A}
\finmulset{A} 
\finmulset{A}
\Bot 
\Bot
A\Perp B 
A\Perp B
A\pinj B 
A\pinj B
\inner{A}{B} 
\inner{A}{B}
\Inner{A}{B} 
\Inner{A}{B}

[edit] Proof trees

Proof trees are described using a postfix syntax and terminated with \DisplayProof

Description Command Example LaTeX source
Axiom node
(for hypotheses) 
\AxRule
 \AxRule{\vdash A} \DisplayProof 
  \AxRule{\vdash A}
  \DisplayProof
Nullary rule
(for logical axioms) 
\NulRule
 \NulRule{A \vdash A} \DisplayProof 
  \NulRule{A \vdash A}
  \DisplayProof
Unary rule 
\UnaRule
 \AxRule{\vdash \wn\Gamma, A} \UnaRule{\vdash \wn\Gamma, \oc A} \DisplayProof 
  \AxRule{\vdash \wn\Gamma, A}
  \UnaRule{\vdash \wn\Gamma, \oc A}
  \DisplayProof
Binary rule 
\BinRule
 \AxRule{\Gamma\vdash A} \AxRule{\Delta,A\vdash C} \BinRule{\Gamma,\Delta\vdash C} \DisplayProof 
  \AxRule{\Gamma\vdash A}
  \AxRule{\Delta,A\vdash C}
  \BinRule{\Gamma,\Delta\vdash C}
  \DisplayProof
Ternary rule 
\TriRule
 \AxRule{\vdash A} \AxRule{\vdash B} \AxRule{\vdash C} \TriRule{\vdash A\land B\land C} \DisplayProof 
  \AxRule{\vdash A}
  \AxRule{\vdash B}
  \AxRule{\vdash C}
  \TriRule{\vdash A\land B\land C}
  \DisplayProof
Label
(before any of the above) 
\LabelRule
 \AxRule{\Gamma\vdash A} \AxRule{\Delta,A\vdash C} \LabelRule{\rulename{cut}} \BinRule{\Gamma,\Delta\vdash C} \DisplayProof 
  \AxRule{\Gamma\vdash A}
  \AxRule{\Delta,A\vdash C}
  \LabelRule{\rulename{cut}}
  \BinRule{\Gamma,\Delta\vdash C}
  \DisplayProof
Proof ellipsis
(two arguments !) 
\VdotsRule
 \AxRule{[A]} \VdotsRule{\pi}{B} \UnaRule{A\imp B} \DisplayProof 
  \AxRule{[A]}
  \VdotsRule{\pi}{B}
  \UnaRule{A\imp B}
  \DisplayProof
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