proof-by-refutation-1 (math concept)
See also
python declaration class | python inclusion class | python sample
Definition
proof-by-refutation-1 is the inference-rule:
\[\left( \boldsymbol{\mathcal{H}} \: \textit{assume} \: \boldsymbol{P}, Inc\left( \boldsymbol{\mathcal{H}} \right) \right) \vdash \neg \boldsymbol{P}\]
Where:
\(\boldsymbol{\mathcal{H}}\) is an hypothesis
\(\boldsymbol{P}\) is a formula-statement
\(\mathit{Inc}\) is the inconsistency function
In plain language, it consists in posing the hypothesis that a proposition \(\boldsymbol{P}\) is true, refuting that hypothesis by proving \(\neg \boldsymbol{P}\), inferring the inconsistency of that hypothesis from this contradiction, and finally inferring \(\boldsymbol{P}\) (or alternatively that the parent theory is itself inconsistent).
Note
Note the possibility that the base theory-derivation from which the hypothesis is elaborated is inconsistent.