ALL_EL_CONV : conv -> conv
STRUCTURE
SYNOPSIS
Computes by inference the result of applying a predicate to elements of a list.
DESCRIPTION
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')
SEEALSO
HOL  Kananaskis-14