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• Bed-mk1

Mk-op-x-false

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

Signature

(mk-op-x-false op left) → bed

Arguments

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

left — First argument to the operator (a bed).

Definitions and Theorems

Function: mk-op-x-false

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

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

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