deductive reasoning, deduction
sequent
hypothesis/context/antecedent ⊢ conclusion/consequence/succedent
logical framework
deductive system,
natural deduction
sequent calculus
inductive reasoning
induction, recursion
inductive type, higher inductive type
In logic (such as sequent calculus or natural deduction) a hypothesis or premise is the antecedent of a sequent (or part of one).