In this paper, we make two major contributions: First, to enhance Boolean learning, we propose a new class of logic implications called extended forward implications. Using a novel concept called implication-frontier, extended forward implications efficiently capture those non-trivial relationships which previous techniques failed to identify. Secondly, we introduce the concept of dual recurrence relations in sequential circuits, and propose a new theorem which uses this concept to quickly identify sequentially untestable faults. Our tool based on the proposed extended forward implications and the new theorem was applied to identify untestable faults in benchmark circuits. Significantly more untestable faults than reported by earlier techniques, low memory overhead and low computational complexity are the noteworthy features of our tool.