Considering the classical definition of faith (notitia, assensus, and fiducia) in the light of both Gordon Clark's formulation (n, a, f as a subset of a), and John Ball's answer to Why does the Covenant of Works not require faith but obedience?, several points come to mind:
a) Adam had both knowledge and agreement concerning the facts of His creation.
b) Adam was expected (via a pointed lesson) to show his trust by obeying.
c) Prior to his fall, Adam was trusting (dependent on) God.
d) The cause of his (our) Fall was his turning away (rebelling) from God, and trusting in himself.
So, despite Clark's seeming semantics, I believe that (along with orthodoxy) notitia and assensus must be conjoined with fiducia in order for saving faith to exist. Adam didn't lose (a); he apostatized by redirecting his trust. Thus, we too must have all three components of faith. God tried his creation, whether they would freely trust Him (live and move, and have their being - mental, physical, and spiritual). Man, though created righteous, was not infallible, was not perfect; in short, was not God! Thank God for the Covenant of Redemption, wherein a people where chosen. Unless the Holy Spirit regenerate the elect, we would not be able to enjoy the triune faith (in our triune God). Let the Bride of Christ thankfully rejoice in the quikening and sustaining power of the Holy Spirit working in them to do His pleasure. Let us cry out Lord, I believe; help thou my unbelief!
See: John Ball - A Treatise of the Covenant of Grace , p. 12.
Gordon H. Clark - Today's Evangelism: Counterfeit or Genuine?, Chapter 6: Faith