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subst-expr

books/system/subst-expr

Included Books

sublis-var pseudo-termp-lemmas subst-var
other
(in-package "ACL2")
include-book
(include-book "sublis-var")
local
(local (include-book "pseudo-termp-lemmas"))
include-book
(include-book "subst-var")
other
(verify-termination subst-expr1
  (declare (xargs :verify-guards nil)))
local
(local (defun subst-expr1-flg
    (flg new old x)
    (cond (flg (cond ((endp x) nil)
          (t (cons (subst-expr1-flg nil new old (car x))
              (subst-expr1-flg t new old (cdr x))))))
      (t (cond ((equal x old) new)
          ((variablep x) x)
          ((fquotep x) x)
          (t (cons-term (ffn-symb x)
              (subst-expr1-flg t new old (fargs x)))))))))
local
(local (defthmd subst-expr1-flg-property
    (equal (subst-expr1-flg flg new old x)
      (if flg
        (subst-expr1-lst new old x)
        (subst-expr1 new old x)))))
local
(local (defthm subst-expr1-flg-preserves-len
    (implies flg
      (equal (len (subst-expr1-flg flg vars terms x)) (len x)))))
local
(local (defthm pseudo-termp-subst-expr1-flg
    (implies (and (pseudo-termp new)
        (pseudo-termp old)
        (if flg
          (pseudo-term-listp x)
          (pseudo-termp x)))
      (if flg
        (pseudo-term-listp (subst-expr1-flg flg new old x))
        (pseudo-termp (subst-expr1-flg flg new old x))))
    :rule-classes nil))
pseudo-term-listp-subst-expr1-lsttheorem
(defthm pseudo-term-listp-subst-expr1-lst
  (implies (and (pseudo-termp new)
      (pseudo-termp old)
      (pseudo-term-listp args))
    (pseudo-term-listp (subst-expr1-lst new old args)))
  :hints (("Goal" :in-theory (enable subst-expr1-flg-property)
     :use ((:instance pseudo-termp-subst-expr1-flg (flg t) (x args))))))
pseudo-term-listp-subst-expr1theorem
(defthm pseudo-term-listp-subst-expr1
  (implies (and (pseudo-termp new)
      (pseudo-termp old)
      (pseudo-termp term))
    (pseudo-termp (subst-expr1 new old term)))
  :hints (("Goal" :in-theory (enable subst-expr1-flg-property)
     :use ((:instance pseudo-termp-subst-expr1-flg (flg nil) (x term))))))
other
(verify-guards subst-expr1)
other
(verify-termination subst-expr-error)
other
(verify-guards subst-expr-error)
other
(verify-termination subst-expr)