deductive reasoning, deduction

sequent

hypothesis/context/antecedent $\vdash$ 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).