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• Integer-operations

Int-lesseq

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

Signature

(int-lesseq operand-left operand-right) → result

Arguments

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

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

Returns

result — Type (boolean-valuep result).

Definitions and Theorems

Function: int-lesseq

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

Theorem: boolean-valuep-of-int-lesseq

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

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

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

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

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

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

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

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

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