Is there a name for the following inference rule?:
If (p => q), then we infer [for all r]: (p and r) => q
If so, what is it?
I use the above inference rule so often, it would be handy (efficient) from a documentation point-of-view, to be able to accompany its use with just a name.
I know that this rule is intuitively obvious, and that the proof of it is trivial, but sometimes a comment taking the form of a rule name can stop the reader going off on a tangent in trying to understand how a logic argument has proceeded from one line to the next (especially, if the various terms involved are complicated expressions).
The various 'logic' sites that I looked at, didn't include this rule in their lists of named inference rules (perhaps, because it is readily deduced from some of the ones that were listed).
Of the many sites I tried, the following two Wikipedia sites seemed to have the most comprehensive listing of inference rules:
http://en.wikipedia.org/wiki/List_of_rules_of_inference#Table:_Rules_of_Inference
http://en.wikipedia.org/wiki/Propositional_calculus#Basic_and_derived_argument_forms
P.S. As an aside, if anyone knows of a site that has a listing of named inference rules more comprehensive than the listings provided by the above-mentioned Wikipedia sites, I'd definitely be interested.
The "proof theoretic" version of this rule is called weakening. I think it would be acceptable to refer to your version of the rule by the same name.