• 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
                • Float-greateq
                • Double-lesseq
                • Double-greateq
                • Double-great
                • Float-lesseq
                • Float-less
                • Float-great
                • Double-less
                • Float-sub
                • Float-rem
                • Float-neq
                • Float-mul
                • Double-sub
                • Double-rem
                • Double-neq
                • Double-mul
                • Double-eq
                • Double-div
                • Double-add
                • Float-eq
                • Float-div
                • Float-add
                • Double-plus
                • Double-minus
                • Float-plus
                • Float-minus
              • 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

• Floating-point-operations

Double-neq

Non-equality != on doubles [JLS14:4.2.4] [JLS14:15.21.1].

Signature

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

Arguments

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

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

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: double-neq

(defun double-neq (operand-left operand-right)
  (declare (xargs :guard (and (double-valuep operand-left)
                              (double-valuep operand-right))))
  (b* ((x (double-value->double operand-left))
       (y (double-value->double operand-right)))
    (boolean-value (double-neq-abs x y))))

Theorem: boolean-valuep-of-double-neq

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

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

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

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

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

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

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

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

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