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• Integer-format-templates

Sinteger-bit-roles-inc-n

List of n signed integer value bit roles, starting with exponent 0, in increasing exponent order.

Signature

(sinteger-bit-roles-inc-n n) → roles

Arguments

n — Guard (natp n).

Returns

roles — Type (sinteger-bit-role-listp roles).

Definitions and Theorems

Function: sinteger-bit-roles-inc-n

(defun sinteger-bit-roles-inc-n (n)
  (declare (xargs :guard (natp n)))
  (b* (((when (zp n)) nil)
       (role (sinteger-bit-role-value (1- n)))
       (roles (sinteger-bit-roles-inc-n (1- n))))
    (append roles (list role))))

Theorem: sinteger-bit-role-listp-of-sinteger-bit-roles-inc-n

(defthm sinteger-bit-role-listp-of-sinteger-bit-roles-inc-n
  (b* ((roles (sinteger-bit-roles-inc-n n)))
    (sinteger-bit-role-listp roles))
  :rule-classes :rewrite)

Theorem: len-of-sinteger-bit-roles-inc-n

(defthm len-of-sinteger-bit-roles-inc-n
  (b* ((?roles (sinteger-bit-roles-inc-n n)))
    (equal (len roles) (nfix n))))

Theorem: sinteger-bit-roles-exponents-of-sinteger-bit-roles-inc-n

(defthm sinteger-bit-roles-exponents-of-sinteger-bit-roles-inc-n
  (equal (sinteger-bit-roles-exponents (sinteger-bit-roles-inc-n n))
         (integers-from-to 0 (1- (nfix n)))))

Theorem: sinteger-bit-roles-value-count-of-sinteger-bit-roles-inc-n

(defthm sinteger-bit-roles-value-count-of-sinteger-bit-roles-inc-n
  (equal
       (sinteger-bit-roles-value-count (sinteger-bit-roles-inc-n n))
       (nfix n)))

Theorem: sinteger-bit-roles-sign-count-of-sinteger-bit-roles-inc-n

(defthm sinteger-bit-roles-sign-count-of-sinteger-bit-roles-inc-n
 (equal (sinteger-bit-roles-sign-count (sinteger-bit-roles-inc-n n))
        0))

Theorem: sinteger-bit-roles-inc-n-of-nfix-n

(defthm sinteger-bit-roles-inc-n-of-nfix-n
  (equal (sinteger-bit-roles-inc-n (nfix n))
         (sinteger-bit-roles-inc-n n)))

Theorem: sinteger-bit-roles-inc-n-nat-equiv-congruence-on-n

(defthm sinteger-bit-roles-inc-n-nat-equiv-congruence-on-n
  (implies (acl2::nat-equiv n n-equiv)
           (equal (sinteger-bit-roles-inc-n n)
                  (sinteger-bit-roles-inc-n n-equiv)))
  :rule-classes :congruence)