• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
    • Gl
      • Term-level-reasoning
      • Glmc
      • Other-resources
      • Optimization
      • Reference
        • Def-gl-thm
        • Shape-specs
        • Symbolic-objects
        • Gl-aside
        • Def-gl-param-thm
        • Symbolic-arithmetic
        • Bfr
          • Pbfr-depends-on
          • Bfr-varname-p
          • Bfr-varname-fix
          • Bfr-to-param-space
          • Bfr-depends-on
          • Aig-var-fix
          • Bfr-reasoning
          • Bfr-andc2
          • Bfr-andc1
          • Bfr-unparam-env
          • Bfr-set-var
          • Bfr-nor
          • Bfr-nand
          • Bfr-mode
          • Bfr-equiv
          • Bfr-xor
          • Bfr-iff
          • Bfr-eval
          • Bfr-param-env
          • Bfr-lookup
          • Bfr-env-equiv
          • Bfr-and
          • Bfr-var
          • Bfr-or
          • Bfr-not
          • Bfr-ite
          • Bdd-mode-or-p-true
          • Aig-mode-or-p-true
          • Bfr-case
        • Def-gl-boolean-constraint
        • Gl-mbe
        • Bvec
        • Flex-bindings
        • Auto-bindings
        • Gl-interp
        • Gl-set-uninterpreted
        • Def-gl-clause-processor
        • Def-glcp-ctrex-rewrite
        • ACL2::always-equal
        • Gl-hint
        • Def-gl-rewrite
        • Def-gl-branch-merge
        • Gl-force-check
        • Gl-concretize
        • Gl-assert
        • Gl-param-thm
        • Gl-simplify-satlink-mode
        • Gl-satlink-mode
        • Gl-bdd-mode
        • Gl-aig-bddify-mode
        • Gl-fraig-satlink-mode
      • Debugging
      • Basic-tutorial
    • Witness-cp
    • Ccg
    • Install-not-normalized
    • Rewrite$
    • Removable-runes
    • Fgl
    • Efficiency
    • Rewrite-bounds
    • Bash
    • Def-dag-measure
    • Bdd
    • Remove-hyps
    • Contextual-rewriting
    • Simp
    • Rewrite$-hyps
    • Bash-term-to-dnf
    • Use-trivial-ancestors-check
    • Minimal-runes
    • Clause-processor-tools
    • Fn-is-body
    • Without-subsumption
    • Rewrite-equiv-hint
    • Def-bounds
    • Rewrite$-context
    • Try-gl-concls
    • Hint-utils
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Bfr

Bfr-varname-p

Signature

(bfr-varname-p x) → *

Definitions and Theorems

Function: bfr-varname-p

(defun bfr-varname-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'bfr-varname-p))
    (declare (ignorable __function__))
    (bfr-case :bdd (natp x)
              :aig (acl2::aig-var-p x))))

Function: bfr-varname-fix

(defun bfr-varname-fix (x)
  (declare (xargs :guard (bfr-varname-p x)))
  (let ((__function__ 'bfr-varname-fix))
    (declare (ignorable __function__))
    (bfr-case :bdd (nfix x)
              :aig (aig-var-fix x))))

Theorem: bfr-varname-p-of-bfr-varname-fix

(defthm bfr-varname-p-of-bfr-varname-fix
  (b* ((new-x (bfr-varname-fix x)))
    (bfr-varname-p new-x))
  :rule-classes :rewrite)

Theorem: bfr-varname-fix-when-bfr-varname-p

(defthm bfr-varname-fix-when-bfr-varname-p
  (implies (bfr-varname-p x)
           (equal (bfr-varname-fix x) x)))

Function: bfr-varname-equiv$inline

(defun bfr-varname-equiv$inline (x y)
  (declare (xargs :guard (and (bfr-varname-p x)
                              (bfr-varname-p y))))
  (equal (bfr-varname-fix x)
         (bfr-varname-fix y)))

Theorem: bfr-varname-equiv-is-an-equivalence

(defthm bfr-varname-equiv-is-an-equivalence
  (and (booleanp (bfr-varname-equiv x y))
       (bfr-varname-equiv x x)
       (implies (bfr-varname-equiv x y)
                (bfr-varname-equiv y x))
       (implies (and (bfr-varname-equiv x y)
                     (bfr-varname-equiv y z))
                (bfr-varname-equiv x z)))
  :rule-classes (:equivalence))

Theorem: bfr-varname-equiv-implies-equal-bfr-varname-fix-1

(defthm bfr-varname-equiv-implies-equal-bfr-varname-fix-1
  (implies (bfr-varname-equiv x x-equiv)
           (equal (bfr-varname-fix x)
                  (bfr-varname-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: bfr-varname-fix-under-bfr-varname-equiv

(defthm bfr-varname-fix-under-bfr-varname-equiv
  (bfr-varname-equiv (bfr-varname-fix x)
                     x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: nfix-of-bfr-varname-fix

(defthm nfix-of-bfr-varname-fix
  (equal (nfix (bfr-varname-fix x))
         (nfix x)))

Theorem: bfr-varname-fix-of-nfix

(defthm bfr-varname-fix-of-nfix
  (equal (bfr-varname-fix (nfix x))
         (nfix x)))

Theorem: bfr-varname-p-when-natp

(defthm bfr-varname-p-when-natp
  (implies (natp x) (bfr-varname-p x)))