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subst-var

books/system/subst-var

Included Books

sublis-var pseudo-termp-lemmas
other
(in-package "ACL2")
include-book
(include-book "sublis-var")
local
(local (include-book "pseudo-termp-lemmas"))
other
(verify-termination subst-var
  (declare (xargs :verify-guards nil)))
local
(local (defun subst-var-flg
    (flg new old x)
    (cond (flg (cond ((endp x) nil)
          (t (cons (subst-var-flg nil new old (car x))
              (subst-var-flg t new old (cdr x))))))
      (t (cond ((variablep x) (cond ((eq x old) new) (t x)))
          ((fquotep x) x)
          (t (cons-term (ffn-symb x) (subst-var-flg t new old (fargs x)))))))))
local
(local (defthmd subst-var-flg-property
    (equal (subst-var-flg flg new old x)
      (if flg
        (subst-var-lst new old x)
        (subst-var new old x)))))
local
(local (defthm subst-var-flg-preserves-len
    (implies flg
      (equal (len (subst-var-flg flg vars terms x)) (len x)))))
local
(local (defthm pseudo-termp-subst-var-flg
    (implies (and (pseudo-termp new)
        (variablep old)
        (if flg
          (pseudo-term-listp x)
          (pseudo-termp x)))
      (if flg
        (pseudo-term-listp (subst-var-flg flg new old x))
        (pseudo-termp (subst-var-flg flg new old x))))
    :rule-classes nil))
pseudo-term-listp-subst-var-lsttheorem
(defthm pseudo-term-listp-subst-var-lst
  (implies (and (pseudo-termp new)
      (variablep old)
      (pseudo-term-listp l))
    (pseudo-term-listp (subst-var-lst new old l)))
  :hints (("Goal" :in-theory (enable subst-var-flg-property)
     :use ((:instance pseudo-termp-subst-var-flg (flg t) (x l))))))
pseudo-termp-subst-vartheorem
(defthm pseudo-termp-subst-var
  (implies (and (pseudo-termp new) (variablep old) (pseudo-termp form))
    (pseudo-termp (subst-var new old form)))
  :hints (("Goal" :in-theory (enable subst-var-flg-property)
     :use ((:instance pseudo-termp-subst-var-flg (flg nil) (x form))))))
other
(verify-guards subst-var)