• Top
  • Documentation
  • Books
  • Boolean-reasoning
    • Ipasir
    • Aignet
    • Aig
    • Satlink
    • Truth
      • Index-permute-shrink
      • Permute-stretch
      • Permute-shrink
      • Env-mismatch-aux
      • Env-permute-shrink
      • Permute-polarity
      • Env-permute-polarity
      • Permute-var-down
      • Env-permute-stretch
      • Swap-vars-aux
      • Swap-vars
      • Permute-var-up
      • Truth-perm-rev
      • Negative-cofactor
      • Index-permute-stretch
      • Env-mismatch
      • Swap-polarity
      • Positive-cofactor
      • Truth-perm
      • Index-perm-rev
      • Nth-set-bit-pos
      • Env-perm-rev
      • Is-xor-with-var
      • Index-swap
      • Index-perm
      • Env-move-var-down
      • Truth-eval
      • Env-swap-vars
      • Env-perm
      • Depends-on-witness
      • Var
      • Index-move-down
      • Env-update
      • Env-swap-polarity
      • Var-repetitions
      • Env-move-var-up
      • Depends-on
      • Index-move-up
      • Truth-norm
      • Index-listp
      • Env-diff-index
      • Env-lookup
      • True
      • False
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Truth

Env-swap-vars

Signature

(env-swap-vars n m env) → swap-env

Arguments

n — first element to swap.
    Guard (natp n).

m — second element to swap.
    Guard (natp m).

env — env to apply the swap to.
    Guard (natp env).

Returns

swap-env — Type (natp swap-env).

Definitions and Theorems

Function: env-swap-vars

(defun env-swap-vars (n m env)
  (declare (xargs :guard (and (natp n) (natp m) (natp env))))
  (let ((__function__ 'env-swap-vars))
    (declare (ignorable __function__))
    (b* ((env (lnfix env))
         (n (lnfix n))
         (m (lnfix m)))
      (env-update n (env-lookup m env)
                  (env-update m (env-lookup n env)
                              env)))))

Theorem: natp-of-env-swap-vars

(defthm natp-of-env-swap-vars
  (b* ((swap-env (env-swap-vars n m env)))
    (natp swap-env))
  :rule-classes :type-prescription)

Theorem: env-swap-vars-commute

(defthm env-swap-vars-commute
  (equal (env-swap-vars m n x)
         (env-swap-vars n m x))
  :rule-classes ((:rewrite :loop-stopper ((n m)))))

Theorem: lookup-in-env-swap-vars

(defthm lookup-in-env-swap-vars
  (b* ((?swap-env (env-swap-vars n m env)))
    (equal (env-lookup k swap-env)
           (env-lookup (index-swap n m k) env))))

Theorem: env-swap-vars-inverse

(defthm env-swap-vars-inverse
  (equal (env-swap-vars n m (env-swap-vars n m env))
         (nfix env)))

Theorem: env-swap-vars-self

(defthm env-swap-vars-self
  (equal (env-swap-vars n n env)
         (nfix env)))

Theorem: env-swap-vars-of-nfix-n

(defthm env-swap-vars-of-nfix-n
  (equal (env-swap-vars (nfix n) m env)
         (env-swap-vars n m env)))

Theorem: env-swap-vars-nat-equiv-congruence-on-n

(defthm env-swap-vars-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (env-swap-vars n m env)
                  (env-swap-vars n-equiv m env)))
  :rule-classes :congruence)

Theorem: env-swap-vars-of-nfix-m

(defthm env-swap-vars-of-nfix-m
  (equal (env-swap-vars n (nfix m) env)
         (env-swap-vars n m env)))

Theorem: env-swap-vars-nat-equiv-congruence-on-m

(defthm env-swap-vars-nat-equiv-congruence-on-m
  (implies (nat-equiv m m-equiv)
           (equal (env-swap-vars n m env)
                  (env-swap-vars n m-equiv env)))
  :rule-classes :congruence)

Theorem: env-swap-vars-of-nfix-env

(defthm env-swap-vars-of-nfix-env
  (equal (env-swap-vars n m (nfix env))
         (env-swap-vars n m env)))

Theorem: env-swap-vars-nat-equiv-congruence-on-env

(defthm env-swap-vars-nat-equiv-congruence-on-env
  (implies (nat-equiv env env-equiv)
           (equal (env-swap-vars n m env)
                  (env-swap-vars n m env-equiv)))
  :rule-classes :congruence)