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\DOC INST
\TYPE {INST : (term * term) list -> thm -> thm}
\SYNOPSIS
Instantiates free variables in a theorem.
\DESCRIBE
When {INST [t1,x1; ...; tn,xn]} is applied to a theorem, it gives a new
theorem that systematically replaces free instances of each variable {xi} with
the corresponding term {ti} in both assumptions and conclusion.
{
A |- t
----------------------------------- INST_TYPE [t1,x1;...;tn,xn]
A[t1,...,tn/x1,...,xn]
|- t[t1,...,tn/x1,...,xn]
}
Bound variables will be renamed if necessary to avoid capture. All variables
are substituted in parallel, so there is no problem if there is an overlap
between the terms {ti} and {xi}.
\FAILURE
Fails if any of the pairs {ti,xi} in the instantiation list has {xi} and {ti}
with different types, or {xi} a non-variable. Multiple instances of the same
{xi} in the list are not trapped, but only the first one will be used
consistently.
\EXAMPLE
Here is a simple example
{
# let th = SPEC_ALL ADD_SYM;;
val th : thm = |- m + n = n + m
# INST [`1`,`m:num`; `x:num`,`n:num`] th;;
val it : thm = |- 1 + x = x + 1
}
\noindent and here is one where bound variable renaming is needed.
{
# let th = SPEC_ALL LE_EXISTS;;
val th : thm = |- m <= n <=> (?d. n = m + d)
# INST [`d:num`,`m:num`] th;;
val it : thm = |- d <= n <=> (?d'. n = d + d')
}
\USES
This is the most efficient way to obtain instances of a theorem; though
sometimes more convenient, {SPEC} and {SPECL} are significantly slower.
\COMMENTS
This is one of HOL Light's 10 primitive inference rules.
\SEEALSO
INST_TYPE, ISPEC, ISPECL, SPEC, SPECL.
\ENDDOC
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