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Field-eq

Field-eq-circuit

Construction of the circuit.

Signature
(field-eq-circuit) → pdef
Returns: pdef — Type (pfcs::definitionp pdef).

This is a PFCS definition with a two relation constraint that call the field-neq and boolean-not circuits. This circuit has an internal variable, which is the result of field-neq and the operand of boolean-not.

Definitions and Theorems

Function: field-eq-circuit

(defun field-eq-circuit nil
 (declare (xargs :guard t))
 (let ((__function__ 'field-eq-circuit))
  (declare (ignorable __function__))
  (pfcs::parse-def
   "field_eq(x, y, z) := {
    field_neq(x, y, w),
    boolean_not(w, z)
    }")))

Theorem: definitionp-of-field-eq-circuit

(defthm definitionp-of-field-eq-circuit
  (b* ((pdef (field-eq-circuit)))
    (pfcs::definitionp pdef))
  :rule-classes :rewrite)

Theorem: sr1cs-definitionp-of-field-eq-circuit

(defthm sr1cs-definitionp-of-field-eq-circuit
  (b* ((pdef (field-eq-circuit)))
    (pfcs::sr1cs-definitionp pdef))
  :rule-classes :rewrite)