• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Svex-compilation
      • Moddb
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
        • Rewriting
        • Svex
        • Bit-blasting
        • Functions
        • 4vmask
        • Why-infinite-width
        • Svex-vars
        • Evaluation
          • Svex-xeval
          • Svex-mono-eval
          • Svex-eval
          • Svex-apply
            • Svex-apply-cases
            • Svex-apply-monotonocity
          • Svex-env
          • Svex-alist-eval
          • Svar-boolmasks-lookup
          • Svex-s4eval
          • Svexlist-unquote
          • Svex-alist-eval-for-symbolic
          • Svexlist-eval
          • Svexlist-quotesp
          • Svar-boolmasks
          • Svexlist-s4eval
          • Svexlist-eval-for-symbolic
        • Values
      • Symbolic-test-vector
      • Vl-to-svex
    • Vwsim
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Svex-apply
• 4vec-<<=

Svex-apply-monotonocity

svex-apply is almost always monotonic :-(

Definitions and Theorems

Theorem: svex-apply-monotonic

(defthm svex-apply-monotonic
  (implies (and (4veclist-<<= x y)
                (not (eq (fnsym-fix fn) '===))
                (or (not (eq (fnsym-fix fn) '===*))
                    (equal (4veclist-nth-safe 1 x)
                           (4veclist-nth-safe 1 y)))
                (or (not (eq (fnsym-fix fn) '==?))
                    (equal (4veclist-nth-safe 1 x)
                           (4veclist-nth-safe 1 y)))
                (or (not (eq (fnsym-fix fn) 'bit?!))
                    (equal (4veclist-nth-safe 0 x)
                           (4veclist-nth-safe 0 y)))
                (or (not (eq (fnsym-fix fn) '?!))
                    (equal (4veclist-nth-safe 0 x)
                           (4veclist-nth-safe 0 y))))
           (4vec-<<= (svex-apply fn x)
                     (svex-apply fn y))))