injectivity : string -> thm
Produce injectivity theorem for an inductive type.
A call injectivity "ty" where "ty" is the name of a recursive type defined
with define_type, returns a ``injectivity'' theorem asserting that elements
constructed by different type constructors are always different. The effect is
exactly the same is if prove_constructors_injective were applied to the
recursion theorem produced by define_type, and the documentation for
prove_constructors_injective gives a lengthier discussion.
- FAILURE CONDITIONS
Fails if ty is not the name of a recursive type, or if all its constructors
# injectivity "num";;
val it : thm = |- !n n'. SUC n = SUC n' <=> n = n'
# injectivity "list";;
val it : thm =
|- !a0 a1 a0' a1'. CONS a0 a1 = CONS a0' a1' <=> a0 = a0' /\ a1 = a1'
- SEE ALSO
cases, define_type, distinctness, prove_constructors_injective.