diff --git a/Notes/MFES/T - Aula 2 - 18 Setembro 2023.md b/Notes/MFES/T - Aula 2 - 18 Setembro 2023.md index b26b941..c857c7a 100644 --- a/Notes/MFES/T - Aula 2 - 18 Setembro 2023.md +++ b/Notes/MFES/T - Aula 2 - 18 Setembro 2023.md @@ -67,16 +67,16 @@ A formula $F$ is: > - $\Gamma \models G$ and $\Gamma$ finite iff $\models \land \Gamma \implies G$. > - - Let $\Gamma = { F_1, F_2, F_3,... }$ be a set of formulas. - $\Gamma$ is *consistent* or *satisfiable* iff there is an assignment that models $\Gamma$. - We say that $\Gamma$ is inconsistent or unsatisfiable iff there is not consistent and denote this by $\Gamma \models \bot$. > [!tip]+ Proposition - > - {$F, \neg F$} \$models \bot$ + > - {$F, \neg F$} $\models \bot$ > - If $\Gamma \models \bot$ and $\Gamma \subseteq \Gamma '$, then $\Gamma ' \models \bot$ > - $\Gamma \models F$ iff $\Gamma, \neg F \models \bot$ -- Formula +- Formula $G$ is a subformula of formula F if it occurs syntactically within F +- Formula G is a strict subformula of F if G is a subformula of $F$ and $G \neg \equals F$ ### 1.2.1 Basic Equivalences 1. $\neg \neg A \equiv A$