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Abstract-syntax-rename

Expr-list-rename

Signature
(expr-list-rename c$::expr-list subst) → fty::result
Arguments: c$::expr-list — Guard (expr-listp c$::expr-list).; subst — Guard (ident-ident-alistp subst).
Returns: fty::result — Type (expr-listp fty::result).

Definitions and Theorems

Theorem: expr-list-rename-type-prescription

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

Theorem: expr-list-rename-when-atom

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

Theorem: expr-list-rename-of-cons

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

Theorem: expr-list-rename-of-append

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

Theorem: consp-of-expr-list-rename

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

Theorem: len-of-expr-list-rename

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

Theorem: nth-of-expr-list-rename

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

Theorem: expr-list-rename-of-revappend

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

Theorem: expr-list-rename-of-reverse

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