#LyX 2.3 created this file. For more info see http://www.lyx.org/ \lyxformat 544 \begin_document \begin_header \save_transient_properties true \origin unavailable \textclass book \use_default_options true \maintain_unincluded_children false \language spanish \language_package default \inputencoding auto \fontencoding global \font_roman "default" "default" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default \default_output_format default \output_sync 0 \bibtex_command default \index_command default \paperfontsize default \spacing single \use_hyperref false \papersize default \use_geometry false \use_package amsmath 1 \use_package amssymb 1 \use_package cancel 1 \use_package esint 1 \use_package mathdots 1 \use_package mathtools 1 \use_package mhchem 1 \use_package stackrel 1 \use_package stmaryrd 1 \use_package undertilde 1 \cite_engine basic \cite_engine_type default \biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification true \use_refstyle 1 \use_minted 0 \index Index \shortcut idx \color #008000 \end_index \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \paragraph_indentation default \is_math_indent 0 \math_numbering_side default \quotes_style swiss \dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Standard Las expresiones, numeradas, están dentro de una caja, que se representa con los tres bordes de arriba, abajo y a la izquierda (a la derecha del número de línea). La caja principal no se suele representar. Si se usa una \emph on Hipótesis \emph default , se crea una nueva caja (dentro de otra), y en cada caja las \emph on Premisas \emph default o \emph on Hipótesis \emph default van al principio y la última línea es la conclusión. Cada caja representa una deducción ( \begin_inset Formula $\vdash$ \end_inset ). \end_layout \begin_layout Section Reglas \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Eliminación de \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Introducción de \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la conjunción \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $E_{\land}:\frac{\vdash\alpha\land\beta}{\vdash\alpha},\frac{\vdash\alpha\land\beta}{\vdash\beta}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $I_{\land}:\frac{\vdash\alpha\,\vdash\beta}{\vdash\alpha\land\beta}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la disyunción \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\underset{\text{Prueba por casos}}{E_{\lor}:\frac{\vdash\alpha\lor\beta\,\vdash(\alpha\vdash\gamma)\,\vdash(\beta\vdash\gamma)}{\vdash\gamma}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $I_{\lor}:\frac{\vdash\alpha}{\vdash\alpha\lor\beta},\frac{\vdash\alpha}{\vdash\beta\lor\alpha}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la implicación \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\underset{\text{Modus Ponens}}{E_{\rightarrow}:\frac{\vdash\alpha\rightarrow\beta\,\vdash\alpha}{\vdash\beta}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\underset{\text{Teorema de la Deducción}}{I_{\rightarrow}:\frac{\vdash(\alpha\vdash\beta)}{\vdash\alpha\rightarrow\beta}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la doble implicación \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $E_{\leftrightarrow}:\frac{\vdash(\alpha\leftrightarrow\beta)}{\vdash(\alpha\rightarrow\beta)},\frac{\vdash(\alpha\leftrightarrow\beta)}{\vdash(\beta\rightarrow\alpha)}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $I_{\leftrightarrow}:\frac{\vdash(\alpha\rightarrow\beta)\,\vdash(\beta\rightarrow\alpha)}{\vdash(\alpha\leftrightarrow\beta)}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la negación \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\underset{\text{Reducción al absurdo}}{E_{\neg}:\frac{\vdash(\neg\alpha\vdash\beta\land\neg\beta)}{\vdash\alpha}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $\underset{\text{Reducción al absurdo}}{I_{\neg}:\frac{\vdash(\alpha\vdash\beta\land\neg\beta)}{\vdash\neg\alpha}}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la doble negación \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $E_{\neg\neg}:\frac{\vdash\neg\neg\alpha}{\vdash\alpha}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout la contradicción \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $CONTRA:\frac{\vdash\alpha\,\vdash\neg\alpha}{\vdash\beta}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \end_layout \end_inset \end_inset \end_layout \begin_layout Standard También la iteración: \begin_inset Formula $IT:\frac{\vdash\alpha}{\vdash\alpha}$ \end_inset , que se usa cuando la hipótesis de una caja es la conclusión, dado que deben estar en líneas distintas. \end_layout \end_body \end_document