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  define_type,   INDUCT_THEN,   new_recursive_definition,   prove_constructors_distinct,   prove_constructors_one_one,   prove_induction_thm,   prove_rec_fn_exists

HOL  Kananaskis 0