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Double-great

Greater-than-or-equal-to comparison > on doubles [JLS14:4.2.4] [JLS14:15.20.1].

Signature

(double-great operand-left operand-right) → result

Arguments

operand-left — Guard (double-valuep operand-left).

operand-right — Guard (double-valuep operand-right).

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: double-great

(defun double-great (operand-left operand-right)
  (declare (xargs :guard (and (double-valuep operand-left)
                              (double-valuep operand-right))))
  (b* ((x (double-value->double operand-left))
       (y (double-value->double operand-right)))
    (boolean-value (double-great-abs x y))))

Theorem: boolean-valuep-of-double-great

(defthm boolean-valuep-of-double-great
  (b* ((result (double-great operand-left operand-right)))
    (boolean-valuep result))
  :rule-classes :rewrite)

Theorem: double-great-of-double-value-fix-operand-left

(defthm double-great-of-double-value-fix-operand-left
  (equal (double-great (double-value-fix operand-left)
                       operand-right)
         (double-great operand-left operand-right)))

Theorem: double-great-double-value-equiv-congruence-on-operand-left

(defthm double-great-double-value-equiv-congruence-on-operand-left
  (implies (double-value-equiv operand-left operand-left-equiv)
           (equal (double-great operand-left operand-right)
                  (double-great operand-left-equiv operand-right)))
  :rule-classes :congruence)

Theorem: double-great-of-double-value-fix-operand-right

(defthm double-great-of-double-value-fix-operand-right
  (equal (double-great operand-left
                       (double-value-fix operand-right))
         (double-great operand-left operand-right)))

Theorem: double-great-double-value-equiv-congruence-on-operand-right

(defthm double-great-double-value-equiv-congruence-on-operand-right
  (implies (double-value-equiv operand-right operand-right-equiv)
           (equal (double-great operand-left operand-right)
                  (double-great operand-left operand-right-equiv)))
  :rule-classes :congruence)