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Pseudo-fn

Pseudo-fn-p

Signature
(pseudo-fn-p x) → *

Definitions and Theorems

Function: pseudo-fn-p

(defun pseudo-fn-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'pseudo-fn-p))
    (declare (ignorable __function__))
    (if (consp x)
        (pseudo-lambda-p x)
      (pseudo-fnsym-p x))))

Theorem: pseudo-fn-p-when-consp

(defthm pseudo-fn-p-when-consp
  (implies (and (pseudo-fn-p x) (consp x))
           (pseudo-lambda-p x)))

Theorem: pseudo-fn-p-when-not-consp

(defthm pseudo-fn-p-when-not-consp
  (implies (and (pseudo-fn-p x) (not (consp x)))
           (pseudo-fnsym-p x)))

Theorem: pseudo-fn-p-when-lambda

(defthm pseudo-fn-p-when-lambda
  (implies (pseudo-lambda-p x)
           (pseudo-fn-p x)))

Theorem: pseudo-fn-p-when-fnsym

(defthm pseudo-fn-p-when-fnsym
  (implies (pseudo-fnsym-p x)
           (pseudo-fn-p x)))