prove_cases_thm : (thm -> thm)

- STRUCTURE
- SYNOPSIS
- Proves a structural cases theorem for an automatically-defined concrete type.
- DESCRIPTION
- 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:prove_cases_thm proves and returns the theorem:
|- !P. (!x. P(LEAF x)) /\ (!b1 b2. P b1 /\ P b2 ==> P(NODE b1 b2)) ==> (!b. P b)

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

- SEEALSO

HOL Kananaskis-14