Prim_rec.prove_case_eq

STRUCTURE

SYNOPSIS

Proves a rewrite for eliminating certain forms of case expression.

DESCRIPTION

If case_def is the definition of a data type’s case constant, where each clause is of the form

   !a1 .. ai f1 .. fm. type_CASE (ctor_i a1 .. ai) f1 .. fm = f_i a1 .. ai

and if nchotomy is a theorem describing how a data type’s values are classified by constructor, of the form

   !v. (?a1 .. ai. v = ctor_1 a1 .. ai) \/
       (?b1 .. bj. v = ctor_2 b1 .. bj) \/
       ...

then a call to prove_case_elim_thm{case_def = case_def, nchotomy = nchotomy} will return a theorem of the form

   (type_CASE u f1 .. fm = v) <=>
     (?a1 .. ai. u = ctor_1 a1 .. ai /\ f1 a1 .. ai = v) \/
     (?b1 .. bj. u = ctor_2 b1 .. bj /\ f2 b1 .. bj = v) \/
     ...

FAILURE

Will fail if the provided theorems are not of the required form. The theorems stored in the TypeBase are of the correct form. The theorem returned by Prim_rec.prove_cases_thm is of the correct form for the nchotomy argument to this function.

SEEALSO

prove_case_elim_thm, prove_case_rand_thm