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• Abstract-syntax-rename

Spec/qual-list-rename

Signature

(spec/qual-list-rename c$::spec/qual-list subst) → fty::result

Arguments

c$::spec/qual-list — Guard (spec/qual-listp c$::spec/qual-list).

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

Returns

fty::result — Type (spec/qual-listp fty::result).

Definitions and Theorems

Theorem: spec/qual-list-rename-type-prescription

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

Theorem: spec/qual-list-rename-when-atom

(defthm spec/qual-list-rename-when-atom
  (implies (atom c$::spec/qual-list)
           (equal (spec/qual-list-rename c$::spec/qual-list subst)
                  nil)))

Theorem: spec/qual-list-rename-of-cons

(defthm spec/qual-list-rename-of-cons
 (equal
      (spec/qual-list-rename (cons c$::spec/qual c$::spec/qual-list)
                             subst)
      (cons (spec/qual-rename c$::spec/qual subst)
            (spec/qual-list-rename c$::spec/qual-list subst))))

Theorem: spec/qual-list-rename-of-append

(defthm spec/qual-list-rename-of-append
  (equal (spec/qual-list-rename (append acl2::x acl2::y)
                                subst)
         (append (spec/qual-list-rename acl2::x subst)
                 (spec/qual-list-rename acl2::y subst))))

Theorem: consp-of-spec/qual-list-rename

(defthm consp-of-spec/qual-list-rename
  (equal (consp (spec/qual-list-rename c$::spec/qual-list subst))
         (consp c$::spec/qual-list)))

Theorem: len-of-spec/qual-list-rename

(defthm len-of-spec/qual-list-rename
  (equal (len (spec/qual-list-rename c$::spec/qual-list subst))
         (len c$::spec/qual-list)))

Theorem: nth-of-spec/qual-list-rename

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

Theorem: spec/qual-list-rename-of-revappend

(defthm spec/qual-list-rename-of-revappend
  (equal (spec/qual-list-rename (revappend acl2::x acl2::y)
                                subst)
         (revappend (spec/qual-list-rename acl2::x subst)
                    (spec/qual-list-rename acl2::y subst))))

Theorem: spec/qual-list-rename-of-reverse

(defthm spec/qual-list-rename-of-reverse
 (equal (spec/qual-list-rename (reverse c$::spec/qual-list)
                               subst)
        (reverse (spec/qual-list-rename c$::spec/qual-list subst))))