A proof obligation (PO) consists of a goal G and a set of hypotheses H. Demonstrating a PO means demonstrating this goal G, under the assumption that all the hypotheses of H are verified.
The hypotheses H are said to be contextual hypotheses.
If the current goal is in the form P ⇒ Q, by application of the deduction principle, P will become a hypothesis and the new goal becomes Q. P is then called a derived hypothesis.
The current hypotheses are composed of the contextual hypotheses and the derived hypotheses.
The hypotheses stack contains all the contextual hypotheses and the derived hypotheses, in the order they appeared.