Rule of Idempotence
Jump to navigation
Jump to search
Theorem
The rule of idempotence is two-fold:
Conjunction
- $p \dashv \vdash p \land p$
Disjunction
- $p \dashv \vdash p \lor p$
Its abbreviation in a tableau proof is $\textrm{Idemp}$.
Also known as
Some sources give this as the rule of tautology or law of tautology, but this is discouraged so as to avoid confusion with the definition of tautology.
Technical Note
When invoking Rule of Idempotence in a tableau proof, use the {{Idempotence}}
template:
{{Idempotence|line|pool|statement|depends|type}}
where:
line
is the number of the line on the tableau proof where Rule of Idempotence is to be invokedpool
is the pool of assumptions (comma-separated list)statement
is the statement of logic that is to be displayed in the Formula column, without the$ ... $
delimitersdepends
is the line (or lines) of the tableau proof upon which this line directly dependstype
is the type of Rule of Idempotence:Disjunction
orConjunction
, whose link will be displayed in the Notes column.