• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-fixpoint-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Moddb
      • Svex-compilation
      • Svmods
        • Address
        • Wire
        • Module
        • Lhs
          • Lhs.lisp
          • Lhs-p
          • Lhs-fix
          • Lhrange
            • Lhrange-fix
            • Lhrange-equiv
            • Lhrange-p
            • Make-lhrange
            • Lhrange-eval
            • Lhrange->atom
            • Lhrange->w
            • Change-lhrange
            • Lhrange->svex
          • Lhs-eval-zero
          • Lhs-equiv
          • Lhs-eval
          • Lhs->svex
        • Svar-add-namespace
        • Path
        • Design
        • Modinst
        • Lhs-add-namespace
        • Modalist
        • Path-add-namespace
        • Modname->submodnames
        • Name
        • Svex-alist-addr-p
        • Constraintlist-addr-p
        • Svar-map-addr-p
        • Lhspairs-addr-p
        • Assigns-addr-p
        • Modname
        • Lhs-addr-p
        • Lhatom-addr-p
        • Modhier-measure
        • Modhier-list-measure
        • Attributes
        • Modhier-list-measure-aux
        • Modhier-loopfreelist-p
        • Modhier-loopfree-p
      • Svstmt
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Testing-utilities
  • Math

• Lhrange

Lhrange->atom

Get the atom field from a lhrange.

Signature

(lhrange->atom x) → atom

Arguments

x — Guard (lhrange-p x).

Returns

atom — Type (lhatom-p atom).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: lhrange->atom$inline

(defun
 lhrange->atom$inline (x)
 (declare (xargs :guard (lhrange-p x)))
 (declare (xargs :guard t))
 (let
  ((__function__ 'lhrange->atom))
  (declare (ignorable __function__))
  (mbe :logic (b* ((x (and t x)))
                  (lhatom-fix (if (and (consp x) (integerp (car x)))
                                  (cdr x)
                                  x)))
       :exec (if (and (consp x) (integerp (car x)))
                 (cdr x)
                 x))))

Theorem: lhatom-p-of-lhrange->atom

(defthm lhatom-p-of-lhrange->atom
        (b* ((atom (lhrange->atom$inline x)))
            (lhatom-p atom))
        :rule-classes :rewrite)

Theorem: lhrange->atom$inline-of-lhrange-fix-x

(defthm lhrange->atom$inline-of-lhrange-fix-x
        (equal (lhrange->atom$inline (lhrange-fix x))
               (lhrange->atom$inline x)))

Theorem: lhrange->atom$inline-lhrange-equiv-congruence-on-x

(defthm lhrange->atom$inline-lhrange-equiv-congruence-on-x
        (implies (lhrange-equiv x x-equiv)
                 (equal (lhrange->atom$inline x)
                        (lhrange->atom$inline x-equiv)))
        :rule-classes :congruence)