• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
    • Gl
    • Witness-cp
    • Ccg
    • Install-not-normalized
    • Rewrite$
    • Fgl
      • Fgl-rewrite-rules
      • Fgl-function-mode
      • Fgl-object
        • Fgl-object-eval
          • Fgl-env
            • Fgl-env-fix
            • Fgl-env-equiv
            • Make-fgl-env
            • Fgl-env->obj-alist
            • Change-fgl-env
            • Fgl-env->bfr-vals
            • Fgl-env-p
          • Bools->int
        • Fgl-object-p
        • G-map
        • G-ite
        • G-cons
        • G-concrete
        • G-apply
        • G-integer
        • Fgl-object-equiv
        • G-boolean
        • G-var
        • Fgl-bitvector
        • Fgl-object-kind
        • Summarize-fgl-object
        • Fgl-make-isomorphic
        • Fgl-object-alist
        • Fgl-objectlist
        • Fgl-object-fix
        • Fgl-object-count
      • Fgl-solving
      • Fgl-handling-if-then-elses
      • Fgl-getting-bits-from-objects
      • Fgl-primitive-and-meta-rules
      • Fgl-counterexamples
      • Fgl-interpreter-overview
      • Fgl-correctness-of-binding-free-variables
      • Fgl-debugging
      • Fgl-testbenches
      • Def-fgl-boolean-constraint
      • Fgl-stack
      • Fgl-rewrite-tracing
      • Def-fgl-param-thm
      • Def-fgl-thm
      • Fgl-fast-alist-support
      • Fgl-array-support
      • Advanced-equivalence-checking-with-fgl
      • Fgl-fty-support
      • Fgl-internals
    • 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

• Fgl-env

Fgl-env-equiv

Basic equivalence relation for fgl-env structures.

Definitions and Theorems

Function: fgl-env-equiv$inline

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

Theorem: fgl-env-equiv-is-an-equivalence

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

Theorem: fgl-env-equiv-implies-equal-fgl-env-fix-1

(defthm fgl-env-equiv-implies-equal-fgl-env-fix-1
  (implies (fgl-env-equiv x x-equiv)
           (equal (fgl-env-fix x)
                  (fgl-env-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: fgl-env-fix-under-fgl-env-equiv

(defthm fgl-env-fix-under-fgl-env-equiv
  (fgl-env-equiv (fgl-env-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-fgl-env-fix-1-forward-to-fgl-env-equiv

(defthm equal-of-fgl-env-fix-1-forward-to-fgl-env-equiv
  (implies (equal (fgl-env-fix x) y)
           (fgl-env-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-fgl-env-fix-2-forward-to-fgl-env-equiv

(defthm equal-of-fgl-env-fix-2-forward-to-fgl-env-equiv
  (implies (equal x (fgl-env-fix y))
           (fgl-env-equiv x y))
  :rule-classes :forward-chaining)

Theorem: fgl-env-equiv-of-fgl-env-fix-1-forward

(defthm fgl-env-equiv-of-fgl-env-fix-1-forward
  (implies (fgl-env-equiv (fgl-env-fix x) y)
           (fgl-env-equiv x y))
  :rule-classes :forward-chaining)

Theorem: fgl-env-equiv-of-fgl-env-fix-2-forward

(defthm fgl-env-equiv-of-fgl-env-fix-2-forward
  (implies (fgl-env-equiv x (fgl-env-fix y))
           (fgl-env-equiv x y))
  :rule-classes :forward-chaining)