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• Fty-pseudo-term-utilities

Fty-check-mv-let-call

FTY version of check-mv-let-call.

Signature

(fty-check-mv-let-call term) 
  → 
(mv yes/no mv-var vars indices hides mv-term body-term)

Arguments

term — Guard (pseudo-termp term).

Returns

yes/no — Type (booleanp yes/no).

mv-var — Type (symbolp mv-var).

vars — Type (symbol-listp vars).

indices — Type (nat-listp indices).

hides — Type (boolean-listp hides).

mv-term — Type (pseudo-termp mv-term).

body-term — Type (pseudo-termp body-term).

Definitions and Theorems

Function: fty-check-mv-let-call

(defun fty-check-mv-let-call (term)
  (declare (xargs :guard (pseudo-termp term)))
  (let ((__function__ 'fty-check-mv-let-call))
    (declare (ignorable __function__))
    (check-mv-let-call (pseudo-term-fix term))))

Theorem: booleanp-of-fty-check-mv-let-call.yes/no

(defthm booleanp-of-fty-check-mv-let-call.yes/no
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: symbolp-of-fty-check-mv-let-call.mv-var

(defthm symbolp-of-fty-check-mv-let-call.mv-var
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (symbolp mv-var))
  :rule-classes :rewrite)

Theorem: symbol-listp-of-fty-check-mv-let-call.vars

(defthm symbol-listp-of-fty-check-mv-let-call.vars
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (symbol-listp vars))
  :rule-classes :rewrite)

Theorem: nat-listp-of-fty-check-mv-let-call.indices

(defthm nat-listp-of-fty-check-mv-let-call.indices
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (nat-listp indices))
  :rule-classes :rewrite)

Theorem: boolean-listp-of-fty-check-mv-let-call.hides

(defthm boolean-listp-of-fty-check-mv-let-call.hides
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (boolean-listp hides))
  :rule-classes :rewrite)

Theorem: pseudo-termp-of-fty-check-mv-let-call.mv-term

(defthm pseudo-termp-of-fty-check-mv-let-call.mv-term
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (pseudo-termp mv-term))
  :rule-classes :rewrite)

Theorem: pseudo-termp-of-fty-check-mv-let-call.body-term

(defthm pseudo-termp-of-fty-check-mv-let-call.body-term
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (pseudo-termp body-term))
  :rule-classes :rewrite)

Theorem: len-of-fty-check-mv-let-call.indices/vars

(defthm len-of-fty-check-mv-let-call.indices/vars
  (implies (and (pseudo-termp term))
           (b* (((mv ?yes/no ?mv-var ?vars
                     ?indices ?hides ?mv-term ?body-term)
                 (fty-check-mv-let-call term)))
             (implies yes/no
                      (equal (len indices) (len vars))))))

Theorem: len-of-fty-check-mv-let-call.hides/vars

(defthm len-of-fty-check-mv-let-call.hides/vars
  (implies (and (pseudo-termp term))
           (b* (((mv ?yes/no ?mv-var ?vars
                     ?indices ?hides ?mv-term ?body-term)
                 (fty-check-mv-let-call term)))
             (implies yes/no
                      (equal (len hides) (len vars))))))

Theorem: pseudo-term-count-of-check-mv-let-call.mv-term

(defthm pseudo-term-count-of-check-mv-let-call.mv-term
  (implies (pseudo-termp term)
           (b* (((mv yes/no & & & & mv-term &)
                 (check-mv-let-call term)))
             (implies yes/no
                      (< (pseudo-term-count mv-term)
                         (pseudo-term-count term)))))
  :rule-classes :linear)

Theorem: pseudo-term-count-of-fty-check-mv-let-call.mv-term

(defthm pseudo-term-count-of-fty-check-mv-let-call.mv-term
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (implies yes/no
             (< (pseudo-term-count mv-term)
                (pseudo-term-count term))))
  :rule-classes :linear)

Theorem: pseudo-term-count-of-check-mv-let-call.body-term

(defthm pseudo-term-count-of-check-mv-let-call.body-term
  (implies (pseudo-termp term)
           (b* (((mv yes/no & & & & & body-term)
                 (check-mv-let-call term)))
             (implies yes/no
                      (< (pseudo-term-count body-term)
                         (pseudo-term-count term)))))
  :rule-classes :linear)

Theorem: pseudo-term-count-of-fty-check-mv-let-call.body-term

(defthm pseudo-term-count-of-fty-check-mv-let-call.body-term
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (implies yes/no
             (< (pseudo-term-count body-term)
                (pseudo-term-count term))))
  :rule-classes :linear)

Theorem: pseudo-term-count-of-check-mv-let-call

(defthm pseudo-term-count-of-check-mv-let-call
  (implies (pseudo-termp term)
           (b* (((mv yes/no & & & & mv-term body-term)
                 (check-mv-let-call term)))
             (implies yes/no
                      (< (+ (pseudo-term-count mv-term)
                            (pseudo-term-count body-term))
                         (pseudo-term-count term)))))
  :rule-classes :linear)

Theorem: pseudo-term-count-if-fty-check-mv-let-call

(defthm pseudo-term-count-if-fty-check-mv-let-call
  (b* (((mv ?yes/no ?mv-var ?vars
            ?indices ?hides ?mv-term ?body-term)
        (fty-check-mv-let-call term)))
    (implies yes/no
             (b* (((mv yes/no & & & & mv-term body-term)
                   (fty-check-mv-let-call term)))
               (implies yes/no
                        (< (+ (pseudo-term-count mv-term)
                              (pseudo-term-count body-term))
                           (pseudo-term-count term))))))
  :rule-classes :linear)