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prove_cases_thm                                             (Prim_rec)
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prove_cases_thm : (thm -> thm)

SYNOPSIS
Proves a structural cases theorem for an automatically-defined concrete type.

DESCRIBE
{prove_cases_thm} takes as its argument a structural induction theorem, in the
form returned by {prove_induction_thm} for an automatically-defined concrete
type.  When applied to such a theorem, {prove_cases_thm} automatically proves
and returns a theorem which states that every value the concrete type in
question is denoted by the value returned by some constructor of the type.

FAILURE
Fails if the argument is not a theorem of the form returned by
{prove_induction_thm}

EXAMPLE
Given the following structural induction theorem for labelled binary trees:

   |- !P. (!x. P(LEAF x)) /\ (!b1 b2. P b1 /\ P b2 ==> P(NODE b1 b2)) ==>
          (!b. P b)

{prove_cases_thm} proves and returns the theorem:

   |- !b. (?x. b = LEAF x) \/ (?b1 b2. b = NODE b1 b2)

This states that every labelled binary tree {b} is either a leaf node
with a label {x} or a tree with two subtrees {b1} and {b2}.

SEEALSO
Prim_rec.INDUCT_THEN, Prim_rec.new_recursive_definition,
Prim_rec.prove_constructors_distinct,
Prim_rec.prove_constructors_one_one, Prim_rec.prove_induction_thm,
Prim_rec.prove_rec_fn_exists.

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