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• Bin-digit

Bin-digit-fix

Fixer for bin-digit.

Signature

(bin-digit-fix x) → fixed-x

Arguments

x — Guard (bin-digitp x).

Returns

fixed-x — Type (bin-digitp fixed-x).

Definitions and Theorems

Function: bin-digit-fix

(defun bin-digit-fix (x)
  (declare (xargs :guard (bin-digitp x)))
  (mbe :logic (if (bin-digitp x) x (char-code #\0))
       :exec x))

Theorem: bin-digitp-of-bin-digit-fix

(defthm bin-digitp-of-bin-digit-fix
  (b* ((fixed-x (bin-digit-fix x)))
    (bin-digitp fixed-x))
  :rule-classes :rewrite)

Theorem: bin-digit-fix-when-bin-digitp

(defthm bin-digit-fix-when-bin-digitp
  (implies (bin-digitp x)
           (equal (bin-digit-fix x) x)))