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• Abstract-syntax-rename

Param-declon-list-rename

Signature

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

Arguments

c$::param-declon-list — Guard (param-declon-listp c$::param-declon-list).

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

Returns

fty::result — Type (param-declon-listp fty::result).

Definitions and Theorems

Theorem: param-declon-list-rename-type-prescription

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

Theorem: param-declon-list-rename-when-atom

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

Theorem: param-declon-list-rename-of-cons

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

Theorem: param-declon-list-rename-of-append

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

Theorem: consp-of-param-declon-list-rename

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

Theorem: len-of-param-declon-list-rename

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

Theorem: nth-of-param-declon-list-rename

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

Theorem: param-declon-list-rename-of-revappend

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

Theorem: param-declon-list-rename-of-reverse

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