inconsistency-introduction-2 (math concept)
See also
python declaration class | python inclusion class | python sample
Definition
inconsistency-introduction-2 is the inference-rule:
\[\left(\left(x = y\right), \left(x \neq y\right)\right) \vdash Inc\left(\mathcal{T}\right)\]
In straightforward language, if we prove both the equality and inequality of two terms, it follows that the theory is inconsistent.
Quotes
A proof of consistency will have to show, by appealing to contentual considerations which are completely unproblematic, that in the formalism in question it is never possible to derive the formula 𝑎 ≠ 𝑎, or alternatively it is not possible to prove both 𝑎 = 𝑏 and 𝑎 ≠ 𝑏. [MGZ21, p. 5]