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• Boolean-operations

Boolean-not

Logical complement ! [JLS14:4.2.5] [JLS14:15.15.6].

Signature

(boolean-not operand) → result

Arguments

operand — Guard (boolean-valuep operand).

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: boolean-not

(defun boolean-not (operand)
  (declare (xargs :guard (boolean-valuep operand)))
  (b* ((x (boolean-value->bool operand)))
    (boolean-value (not x))))

Theorem: boolean-valuep-of-boolean-not

(defthm boolean-valuep-of-boolean-not
  (b* ((result (boolean-not operand)))
    (boolean-valuep result))
  :rule-classes :rewrite)

Theorem: boolean-not-of-boolean-value-fix-operand

(defthm boolean-not-of-boolean-value-fix-operand
  (equal (boolean-not (boolean-value-fix operand))
         (boolean-not operand)))

Theorem: boolean-not-boolean-value-equiv-congruence-on-operand

(defthm boolean-not-boolean-value-equiv-congruence-on-operand
  (implies (boolean-value-equiv operand operand-equiv)
           (equal (boolean-not operand)
                  (boolean-not operand-equiv)))
  :rule-classes :congruence)