• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
    • Gl
    • Witness-cp
    • Ccg
    • Install-not-normalized
    • Rewrite$
    • Fgl
      • Fgl-rewrite-rules
      • Fgl-function-mode
      • Fgl-object
      • Fgl-solving
      • Fgl-handling-if-then-elses
      • Fgl-counterexamples
      • Fgl-getting-bits-from-objects
      • Fgl-primitive-and-meta-rules
      • Fgl-interpreter-overview
      • Fgl-correctness-of-binding-free-variables
      • Fgl-debugging
      • Fgl-testbenches
      • Def-fgl-boolean-constraint
      • Fgl-stack
      • Def-fgl-param-thm
      • Fgl-rewrite-tracing
      • Def-fgl-thm
      • Fgl-fast-alist-support
      • Fgl-array-support
      • Advanced-equivalence-checking-with-fgl
      • Fgl-fty-support
      • Fgl-internals
        • Symbolic-arithmetic
        • Bfr
          • Bfr-eval
          • Bfrstate
          • Bfr->aignet-lit
          • Bfr-p
          • Bounded-lit-fix
          • Bfr-list-fix
          • Aignet-lit->bfr
          • Variable-g-bindings
          • Fgl-object-bindings-bfrs-ok
          • Fgl-object-bindings-bfrlist
          • Bfr-listp$
          • Bfrstate>=
          • Bfr-listp-witness
          • Bfr-set-var
          • Bfr-negate
          • Bfr-fix
          • Fgl-bfr-object-bindings-p
          • Bfr-mode
          • Bfr-mode-is
          • Lbfr-case
          • Bfrstate-case
          • Bfrstate-mode-is
          • Lbfr-mode-is
          • Bfr-mode-p
        • Fgl-interpreter-state
    • Removable-runes
    • 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-list-fix

Signature

(bfr-list-fix x &optional (bfrstate 'bfrstate)) → new-x

Arguments

x — Guard (bfr-listp x).

bfrstate — Guard (bfrstate-p bfrstate).

Returns

new-x — Type (bfr-listp new-x).

Definitions and Theorems

Function: bfr-list-fix-fn

(defun bfr-list-fix-fn (x bfrstate)
  (declare (xargs :guard (and (bfrstate-p bfrstate)
                              (bfr-listp x))))
  (let ((__function__ 'bfr-list-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             x
           (cons (bfr-fix (car x))
                 (bfr-list-fix (cdr x))))
         :exec x)))

Theorem: bfr-listp-of-bfr-list-fix

(defthm bfr-listp-of-bfr-list-fix
  (b* ((new-x (bfr-list-fix-fn x bfrstate)))
    (bfr-listp new-x))
  :rule-classes :rewrite)

Theorem: bfr-list-fix-when-bfr-listp

(defthm bfr-list-fix-when-bfr-listp
  (b* nil
    (implies (bfr-listp x)
             (equal (bfr-list-fix x) x))))

Theorem: car-of-bfr-list-fix

(defthm car-of-bfr-list-fix
  (b* nil
    (implies (consp x)
             (equal (car (bfr-list-fix x))
                    (bfr-fix (car x))))))

Theorem: cdr-of-bfr-list-fix

(defthm cdr-of-bfr-list-fix
  (b* nil
    (implies (consp x)
             (equal (cdr (bfr-list-fix x))
                    (bfr-list-fix (cdr x))))))

Theorem: consp-of-bfr-list-fix

(defthm consp-of-bfr-list-fix
  (b* nil
    (equal (consp (bfr-list-fix x))
           (consp x))))

Theorem: len-of-bfr-list-fix

(defthm len-of-bfr-list-fix
  (b* nil
    (equal (len (bfr-list-fix x)) (len x))))

Theorem: bfr-list-fix-fn-of-bfrstate-fix-bfrstate

(defthm bfr-list-fix-fn-of-bfrstate-fix-bfrstate
  (equal (bfr-list-fix-fn x (bfrstate-fix bfrstate))
         (bfr-list-fix-fn x bfrstate)))

Theorem: bfr-list-fix-fn-bfrstate-equiv-congruence-on-bfrstate

(defthm bfr-list-fix-fn-bfrstate-equiv-congruence-on-bfrstate
  (implies (bfrstate-equiv bfrstate bfrstate-equiv)
           (equal (bfr-list-fix-fn x bfrstate)
                  (bfr-list-fix-fn x bfrstate-equiv)))
  :rule-classes :congruence)