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• Typed-list-utilities
• Nat-list-fix

Nat-list-fix-theorems

Some theorems about the library function nat-list-fix.

Definitions and Theorems

Theorem: cdr-of-nat-list-fix

(defthm cdr-of-nat-list-fix
  (equal (cdr (nat-list-fix x))
         (nat-list-fix (cdr x))))

Theorem: car-of-nat-list-fix-when-consp

(defthm car-of-nat-list-fix-when-consp
  (implies (consp x)
           (equal (car (nat-list-fix x))
                  (nfix (car x)))))

Theorem: car-of-nat-list-fix-iff-consp

(defthm car-of-nat-list-fix-iff-consp
  (iff (car (nat-list-fix x)) (consp x)))

Theorem: rev-of-nat-list-fix

(defthm rev-of-nat-list-fix
  (equal (rev (nat-list-fix x))
         (nat-list-fix (rev x))))

Theorem: nat-list-fix-of-true-list-fix

(defthm nat-list-fix-of-true-list-fix
  (equal (nat-list-fix (true-list-fix x))
         (nat-list-fix x)))