• 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
                • Long-long-ushiftr
                • Long-int-ushiftr
                • Int-long-ushiftr
                • Int-int-ushiftr
                • Long-long-shiftr
                • Long-long-shiftl
                • Long-int-shiftr
                • Long-int-shiftl
                • Int-long-shiftr
                • Int-int-shiftr
                • Int-long-shiftl
                • Int-int-shiftl
                • Long-xor
                • Long-neq
                • Long-lesseq
                • Long-ior
                • Long-greateq
                • Long-and
                • Int-xor
                • Int-ior
                • Int-greateq
                • Long-rem
                • Long-mul
                • Long-less
                • Long-great
                • Long-eq
                • Long-div
                • Long-add
                • Int-neq
                • Int-mul
                • Int-lesseq
                • Int-great
                • Int-eq
                • Int-and
                • Int-add
                • Long-sub
                • Int-sub
                • Int-rem
                • Int-less
                • Int-div
                • Long-plus
                • Long-not
                • Long-minus
                • Int-not
                • Int-minus
                • Int-plus
              • Floating-point-operations
              • Boolean-operations
            • 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

• Integer-operations

Int-neq

Non-equality != on ints [JLS14:4.2.2] [JLS14:15.21.1].

Signature

(int-neq operand-left operand-right) → result

Arguments

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

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

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: int-neq

(defun int-neq (operand-left operand-right)
  (declare (xargs :guard (and (int-valuep operand-left)
                              (int-valuep operand-right))))
  (b* ((x (int-value->int operand-left))
       (y (int-value->int operand-right)))
    (boolean-value (not (equal x y)))))

Theorem: boolean-valuep-of-int-neq

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

Theorem: int-neq-commutative

(defthm int-neq-commutative
  (equal (int-neq x y) (int-neq y x)))

Theorem: int-neq-of-int-value-fix-operand-left

(defthm int-neq-of-int-value-fix-operand-left
  (equal (int-neq (int-value-fix operand-left)
                  operand-right)
         (int-neq operand-left operand-right)))

Theorem: int-neq-int-value-equiv-congruence-on-operand-left

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

Theorem: int-neq-of-int-value-fix-operand-right

(defthm int-neq-of-int-value-fix-operand-right
  (equal (int-neq operand-left
                  (int-value-fix operand-right))
         (int-neq operand-left operand-right)))

Theorem: int-neq-int-value-equiv-congruence-on-operand-right

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