Theory of proveit.logic.booleans¶

Boolean arithmetic. Boolean ($\mathbb{B}$) is the set containing only TRUE ($\top$) and FALSE ($\bot$). This theory contains operations that are defined to act on Boolean elements: implication ($\Rightarrow$, $\Leftrightarrow$), negation ($\neg$), conjunction ($\land$), and disjunction ($\lor$). The quantification operations, universal ($\forall$) and existential ($\exists$), are also defined in this theory because these operate on multiple instances of Boolean values.

In [1]:
import proveit
%theory


Local content of this theory

common expressions axioms theorems demonstrations

Sub-theories

implication Implies and Iff (if and only if) operations Not operation And operation Or operation Forall (universal quantification) and Exists (existential quantification) operations