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• Abstract-syntax-rename

Genassoc-list-rename

Signature

(genassoc-list-rename c$::genassoc-list subst) → fty::result

Arguments

c$::genassoc-list — Guard (genassoc-listp c$::genassoc-list).

subst — Guard (ident-ident-alistp subst).

Returns

fty::result — Type (genassoc-listp fty::result).

Definitions and Theorems

Theorem: genassoc-list-rename-type-prescription

(defthm genassoc-list-rename-type-prescription
  (true-listp (genassoc-list-rename c$::genassoc-list subst))
  :rule-classes :type-prescription)

Theorem: genassoc-list-rename-when-atom

(defthm genassoc-list-rename-when-atom
  (implies (atom c$::genassoc-list)
           (equal (genassoc-list-rename c$::genassoc-list subst)
                  nil)))

Theorem: genassoc-list-rename-of-cons

(defthm genassoc-list-rename-of-cons
  (equal (genassoc-list-rename (cons c$::genassoc c$::genassoc-list)
                               subst)
         (cons (genassoc-rename c$::genassoc subst)
               (genassoc-list-rename c$::genassoc-list subst))))

Theorem: genassoc-list-rename-of-append

(defthm genassoc-list-rename-of-append
  (equal (genassoc-list-rename (append acl2::x acl2::y)
                               subst)
         (append (genassoc-list-rename acl2::x subst)
                 (genassoc-list-rename acl2::y subst))))

Theorem: consp-of-genassoc-list-rename

(defthm consp-of-genassoc-list-rename
  (equal (consp (genassoc-list-rename c$::genassoc-list subst))
         (consp c$::genassoc-list)))

Theorem: len-of-genassoc-list-rename

(defthm len-of-genassoc-list-rename
  (equal (len (genassoc-list-rename c$::genassoc-list subst))
         (len c$::genassoc-list)))

Theorem: nth-of-genassoc-list-rename

(defthm nth-of-genassoc-list-rename
  (equal (nth acl2::n
              (genassoc-list-rename c$::genassoc-list subst))
         (if (< (nfix acl2::n)
                (len c$::genassoc-list))
             (genassoc-rename (nth acl2::n c$::genassoc-list)
                              subst)
           nil)))

Theorem: genassoc-list-rename-of-revappend

(defthm genassoc-list-rename-of-revappend
  (equal (genassoc-list-rename (revappend acl2::x acl2::y)
                               subst)
         (revappend (genassoc-list-rename acl2::x subst)
                    (genassoc-list-rename acl2::y subst))))

Theorem: genassoc-list-rename-of-reverse

(defthm genassoc-list-rename-of-reverse
  (equal (genassoc-list-rename (reverse c$::genassoc-list)
                               subst)
         (reverse (genassoc-list-rename c$::genassoc-list subst))))