• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
      • Event-macros
      • Java
        • Atj
        • Aij
        • Language
          • Syntax
          • Semantics
            • Primitive-function-macros
            • Primitive-values
            • Floating-point-placeholders
            • Pointers
            • Floating-point-value-set-parameters
            • Values
            • Primitive-operations
              • Integer-operations
              • Floating-point-operations
              • Boolean-operations
                • Boolean-xor
                • Boolean-neq
                • Boolean-ior
                • Boolean-eq
                • Boolean-and
                • Boolean-not
            • Primitive-conversions
            • Reference-values
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Number-theory
      • Cryptography
      • Lists-light
      • Builtins
      • Axe
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Boolean-operations

Boolean-eq

Equality == on booleans [JLS14:4.2.5] [JLS14:15.21.2].

Signature

(boolean-eq operand-left operand-right) → result

Arguments

operand-left — Guard (boolean-valuep operand-left).

operand-right — Guard (boolean-valuep operand-right).

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: boolean-eq

(defun boolean-eq (operand-left operand-right)
  (declare (xargs :guard (and (boolean-valuep operand-left)
                              (boolean-valuep operand-right))))
  (b* ((x (boolean-value->bool operand-left))
       (y (boolean-value->bool operand-right)))
    (boolean-value (equal x y))))

Theorem: boolean-valuep-of-boolean-eq

(defthm boolean-valuep-of-boolean-eq
  (b* ((result (boolean-eq operand-left operand-right)))
    (boolean-valuep result))
  :rule-classes :rewrite)

Theorem: boolean-eq-commutative

(defthm boolean-eq-commutative
  (equal (boolean-eq x y)
         (boolean-eq y x)))

Theorem: boolean-eq-of-boolean-value-fix-operand-left

(defthm boolean-eq-of-boolean-value-fix-operand-left
  (equal (boolean-eq (boolean-value-fix operand-left)
                     operand-right)
         (boolean-eq operand-left operand-right)))

Theorem: boolean-eq-boolean-value-equiv-congruence-on-operand-left

(defthm boolean-eq-boolean-value-equiv-congruence-on-operand-left
  (implies (boolean-value-equiv operand-left operand-left-equiv)
           (equal (boolean-eq operand-left operand-right)
                  (boolean-eq operand-left-equiv operand-right)))
  :rule-classes :congruence)

Theorem: boolean-eq-of-boolean-value-fix-operand-right

(defthm boolean-eq-of-boolean-value-fix-operand-right
  (equal (boolean-eq operand-left
                     (boolean-value-fix operand-right))
         (boolean-eq operand-left operand-right)))

Theorem: boolean-eq-boolean-value-equiv-congruence-on-operand-right

(defthm boolean-eq-boolean-value-equiv-congruence-on-operand-right
  (implies (boolean-value-equiv operand-right operand-right-equiv)
           (equal (boolean-eq operand-left operand-right)
                  (boolean-eq operand-left operand-right-equiv)))
  :rule-classes :congruence)