prove_cases_thm : thm -> thm
Proves a structural cases theorem for an automatically-defined concrete type.
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 CONDITIONS
Fails if the argument is not a theorem of the form returned by
The following type definition for labelled binary trees:
returns an induction theorem ith that can then be fed to
# let ith,rth = define_type "tree = LEAF num | NODE tree tree";;
val ith : thm =
|- !P. (!a. P (LEAF a)) /\ (!a0 a1. P a0 /\ P a1 ==> P (NODE a0 a1))
==> (!x. P x)
val rth : thm =
|- !f0 f1.
?fn. (!a. fn (LEAF a) = f0 a) /\
(!a0 a1. fn (NODE a0 a1) = f1 a0 a1 (fn a0) (fn a1))
# prove_cases_thm ith;;
val it : thm = |- !x. (?a. x = LEAF a) \/ (?a0 a1. x = NODE a0 a1)
An easier interface is cases "tree". This function is mainly intended to
generate the cases theorems for that function.
- SEE ALSO
cases, define_type, INDUCT_THEN, new_recursive_definition,
prove_constructors_distinct, prove_constructors_one_one, prove_induction_thm.