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:It returns the theorem
ALL_EL P [x0;...xn]

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] = T

|- 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
- Evaluatingreturns the following theorem:
ALL_EL_CONV bool_EQ_CONV “ALL_EL ($= T) [T;F;T]”;

In general, if the predicate P is an explicit lambda abstraction (\x. P x), the conversion should be in the form|- ALL_EL($= T)[T;F;T] = F

(BETA_CONV THENC conv')

- SEEALSO

HOL Kananaskis-14