\DOC completeInduct_on
\TYPE {completeInduct_on : term quotation -> tactic}
\SYNOPSIS
Perform complete induction
\KEYWORDS
induction, complete.
\DESCRIBE
If {q} parses into a well-typed term {M}, an invocation
{completeInduct_on q} begins a proof by complete (also known as
`course-of-values') induction on {M}. The term {M} should occur free in
the current goal.
\FAILURE
If {M} does not parse into a term or does not occur free in the
current goal.
\EXAMPLE
Suppose we wish to prove that every number not equal to one has a prime
factor:
{
!n. ~(n = 1) ==> ?p. prime p /\ p divides n
}
A natural way to prove this is by complete induction. Invoking
{completeInduct_on `n`} yields the goal
{
{ !m. m < n ==> ~(m = 1) ==> ?p. prime p /\ p divides m }
?~(n = 1) ==> ?p. prime p /\ p divides n
}
\SEEALSO
bossLib.measureInduct_on, bossLib.Induct, bossLib.Induct_on.
\ENDDOC