ACL2-PC_colon__colon_GENEQV.html -- ACL2 Version 6.3

### ACL2-PC::GENEQV

(macro) `` show the generated equivalence relation maintained at the current subterm

    Major Section:  PROOF-CHECKER-COMMANDS

    General Forms:
    geneqv     ; show list of equivalence relations being maintained
    (geneqv t) ; as above, but pair each relation with a justifying rune

This is an advanced command, whose effect is to print the so-called ``generated equivalence relation'' (or ``geneqv'') that is maintained at the current subterm of the conclusion. That structure is a list of equivalence relations, representing the transitive closure `E` of the union of those relations, such that it suffices to maintain `E` at the current subterm: if that subterm, `u`, is replaced in the goal's conclusion, `G`, by another term equivalent to `u` with respect to `E`, then the resulting conclusion is Boolean equivalent to `G`. Also see defcong.

The command ``geneqv`' prints the above list of equivalence relations, or more precisely, the list of function symbols for those relations. If however `geneqv` is given a non-`nil` argument, then a list is printed whose elements are each of the form `(s r)`, where `s` is the symbol for an equivalence relation and `r` is a `:``congruence` rune justifying the inclusion of `s` in the list of equivalence relations being maintained at the current subterm.