ALL_EL_CONV

listLib.ALL_EL_CONV : conv -> conv

Computes by inference the result of applying a predicate to elements of a list.

ALL_EL_CONV takes a conversion conv and a term tm in the following form:

   ALL_EL P [x0;...xn]

It returns the theorem

   |- ALL_EL P [x0;...xn] = T

if for every xi occurring in the list, conv “P xi” returns a theorem |- P xi = T, otherwise, if for at least one xi, evaluating conv “P xi” returns the theorem |- P xi = F, then it returns the theorem

   |- ALL_EL P [x0;...xn] = F

Failure

ALL_EL_CONV conv tm fails if tm is not of the form described above, or failure occurs when evaluating conv “P xi” for some xi.

Example

Evaluating

   ALL_EL_CONV bool_EQ_CONV “ALL_EL ($= T) [T;F;T]”;

returns the following theorem:

   |- ALL_EL($= T)[T;F;T] = F

In general, if the predicate P is an explicit lambda abstraction (\x. P x), the conversion should be in the form

   (BETA_CONV THENC conv')

See also

listLib.SOME_EL_CONV, listLib.IS_EL_CONV, listLib.FOLDL_CONV, listLib.FOLDR_CONV, listLib.list_FOLD_CONV