• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • 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
    • Taspi
    • Riscv
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
  • Macro-libraries
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Integer-operations

Long-great

Greater-than comparison > on longs [JLS14:4.2.2] [JLS14:15.20.1].

Signature

(long-great operand-left operand-right) → result

Arguments

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

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

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: long-great

(defun long-great (operand-left operand-right)
  (declare (xargs :guard (and (long-valuep operand-left)
                              (long-valuep operand-right))))
  (b* ((x (long-value->int operand-left))
       (y (long-value->int operand-right)))
    (boolean-value (> x y))))

Theorem: boolean-valuep-of-long-great

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

Theorem: long-great-of-long-value-fix-operand-left

(defthm long-great-of-long-value-fix-operand-left
  (equal (long-great (long-value-fix operand-left)
                     operand-right)
         (long-great operand-left operand-right)))

Theorem: long-great-long-value-equiv-congruence-on-operand-left

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

Theorem: long-great-of-long-value-fix-operand-right

(defthm long-great-of-long-value-fix-operand-right
  (equal (long-great operand-left
                     (long-value-fix operand-right))
         (long-great operand-left operand-right)))

Theorem: long-great-long-value-equiv-congruence-on-operand-right

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