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      • Term
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• Pseudo-term-lambda

Pseudo-term-lambda->body

Accessor for the lambda body of a lambda call pseudo-term.

Signature

(pseudo-term-lambda->body x) → body

Arguments

x — Guard (pseudo-termp x).

Returns

body — Type (pseudo-termp body).

Definitions and Theorems

Function: pseudo-term-lambda->body

(defun pseudo-term-lambda->body (x)
  (declare (xargs :guard (pseudo-termp x)))
  (declare (xargs :guard (eq (pseudo-term-kind x) :lambda)))
  (let ((__function__ 'pseudo-term-lambda->body))
    (declare (ignorable __function__))
    (mbe :logic (and (eq (pseudo-term-kind x) :lambda)
                     (pseudo-term-fix (caddr (car x))))
         :exec (caddr (car x)))))

Theorem: pseudo-termp-of-pseudo-term-lambda->body

(defthm pseudo-termp-of-pseudo-term-lambda->body
  (b* ((body (pseudo-term-lambda->body x)))
    (pseudo-termp body))
  :rule-classes :rewrite)

Theorem: pseudo-lambda->body-of-pseudo-term-lambda->fn

(defthm pseudo-lambda->body-of-pseudo-term-lambda->fn
  (equal (pseudo-lambda->body (pseudo-term-lambda->fn x))
         (pseudo-term-lambda->body x)))

Theorem: acl2-count-of-pseudo-term-lambda->body

(defthm acl2-count-of-pseudo-term-lambda->body
 (implies (equal (pseudo-term-kind x) :lambda)
          (< (acl2-count (pseudo-term-lambda->body x))
             (acl2-count (pseudo-term-fix x))))
 :rule-classes
 ((:linear
       :trigger-terms ((acl2-count (pseudo-term-lambda->body x))))))

Theorem: pseudo-term-lambda->body-of-pseudo-term-fix-x

(defthm pseudo-term-lambda->body-of-pseudo-term-fix-x
  (equal (pseudo-term-lambda->body (pseudo-term-fix x))
         (pseudo-term-lambda->body x)))

Theorem: pseudo-term-lambda->body-pseudo-term-equiv-congruence-on-x

(defthm pseudo-term-lambda->body-pseudo-term-equiv-congruence-on-x
  (implies (pseudo-term-equiv x x-equiv)
           (equal (pseudo-term-lambda->body x)
                  (pseudo-term-lambda->body x-equiv)))
  :rule-classes :congruence)