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• Patterns

Similar-patternsp

(similar-patternsp pat1 pat2) determines whether pat1 and pat2 are compatible with the same data.

Definitions and Theorems

Function: similar-patternsp

(defun similar-patternsp (pat1 pat2)
       (declare (xargs :guard t))
       (if pat1
           (and pat2
                (if (atom pat1)
                    (atom pat2)
                    (and (consp pat2)
                         (similar-patternsp (car pat1)
                                            (car pat2))
                         (similar-patternsp (cdr pat1)
                                            (cdr pat2)))))
           (not pat2)))

Theorem: similar-patternsp-commutes

(defthm similar-patternsp-commutes
        (implies (similar-patternsp pat2 pat1)
                 (similar-patternsp pat1 pat2)))

Theorem: similar-patternsp-self

(defthm similar-patternsp-self
        (similar-patternsp x x))

Theorem: similar-patternsp-is-an-equivalence

(defthm similar-patternsp-is-an-equivalence
        (and (booleanp (similar-patternsp x y))
             (similar-patternsp x x)
             (implies (similar-patternsp x y)
                      (similar-patternsp y x))
             (implies (and (similar-patternsp x y)
                           (similar-patternsp y z))
                      (similar-patternsp x z)))
        :rule-classes (:equivalence))

Theorem: similar-patternsp-implies-iff-data-for-patternp-1

(defthm similar-patternsp-implies-iff-data-for-patternp-1
        (implies (similar-patternsp x x-equiv)
                 (iff (data-for-patternp x y)
                      (data-for-patternp x-equiv y)))
        :rule-classes (:congruence))

Theorem: similar-patternsp-implies-iff-data-for-patternp-2

(defthm similar-patternsp-implies-iff-data-for-patternp-2
        (implies (similar-patternsp y y-equiv)
                 (iff (data-for-patternp x y)
                      (data-for-patternp x y-equiv)))
        :rule-classes (:congruence))