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Integer-operations

Long-lesseq

Less-than-or-equal-to comparison <= on longs [JLS14:4.2.2] [JLS14:15.20.1].

Signature
(long-lesseq operand-left operand-right) → result
Arguments: operand-left — Guard (long-valuep operand-left).; operand-right — Guard (long-valuep operand-right).
Returns: result — Type (boolean-valuep result).

Definitions and Theorems

Function: long-lesseq

(defun long-lesseq (operand-left operand-right)
  (declare (xargs :guard (and (long-valuep operand-left)
                              (long-valuep operand-right))))
  (b* ((x (long-value->int operand-left))
       (y (long-value->int operand-right)))
    (boolean-value (<= x y))))

Theorem: boolean-valuep-of-long-lesseq

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

Theorem: long-lesseq-of-long-value-fix-operand-left

(defthm long-lesseq-of-long-value-fix-operand-left
  (equal (long-lesseq (long-value-fix operand-left)
                      operand-right)
         (long-lesseq operand-left operand-right)))

Theorem: long-lesseq-long-value-equiv-congruence-on-operand-left

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

Theorem: long-lesseq-of-long-value-fix-operand-right

(defthm long-lesseq-of-long-value-fix-operand-right
  (equal (long-lesseq operand-left
                      (long-value-fix operand-right))
         (long-lesseq operand-left operand-right)))

Theorem: long-lesseq-long-value-equiv-congruence-on-operand-right

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