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• Bed-mk1

Mk-op-false-x

Construct a reduced BED for op(false, right).

Signature

(mk-op-false-x op right) → bed

Arguments

op — The operator being applied.
    Guard (bed-op-p op).

right — Second argument to the operator (a bed).

Definitions and Theorems

Function: mk-op-false-x

(defun mk-op-false-x (op right)
  (declare (xargs :guard (bed-op-p op)))
  (let ((__function__ 'mk-op-false-x))
    (declare (ignorable __function__))
    (b* ((op (bed-op-fix$ op))
         ((when (eql op (bed-op-true))) t)
         ((when (eql op (bed-op-ior))) right)
         ((when (eql op (bed-op-orc2)))
          (mk-not right))
         ((when (eql op (bed-op-arg1))) nil)
         ((when (eql op (bed-op-orc1))) t)
         ((when (eql op (bed-op-arg2))) right)
         ((when (eql op (bed-op-eqv)))
          (mk-not right))
         ((when (eql op (bed-op-and))) nil)
         ((when (eql op (bed-op-nand))) t)
         ((when (eql op (bed-op-xor))) right)
         ((when (eql op (bed-op-not2)))
          (mk-not right))
         ((when (eql op (bed-op-andc2))) nil)
         ((when (eql op (bed-op-not1))) t)
         ((when (eql op (bed-op-andc1))) right)
         ((when (eql op (bed-op-nor)))
          (mk-not right))
         ((when (eql op (bed-op-false))) nil))
      (mk-op-raw op nil right))))

Theorem: bed-eval-of-mk-op-false-x

(defthm bed-eval-of-mk-op-false-x
  (equal (bed-eval (mk-op-false-x op right) env)
         (bed-eval (mk-op-raw op nil right)
                   env)))