**Description: **Define Russell's
definition description binder, which can be read as
"the unique such that ," where ordinarily contains
as a free
variable. Our definition is meaningful only when there
is exactly one
such that is
true (see iotaval 5246);
otherwise, it evaluates to the empty set (see iotanul 5250). Russell used
the inverted iota symbol to represent the binder.
Sometimes proofs need to expand an iota-based definition. That is,
given "X = the x for which ... x ... x ..." holds, the proof
needs to
get to "... X ... X ...". A general strategy to do this is
to use
riotacl2 6334 (or iotacl 5258 for unbounded iota), as demonstrated in the
proof of supub 7226. This can be easier than applying riotasbc 6336 or a
version that applies an explicit substitution, because substituting an
iota into its own property always has a bound variable clash which must
be first renamed or else guarded with NF.
(Contributed by Andrew Salmon, 30-Jun-2011.) |