In , is a theorem of less importance which can be readily deduced from a previous, more notable statement. A corollary could, for instance, be a proposition which is incidentally proved while proving another proposition; it might also be used more casually to refer to something which naturally or incidentally accompanies something else e.g., violence as a corollary of revolutionary social changes.
Charles Sanders Peirce held that the most important division of kinds of deductive reasoning is that between corollarial & theorematic. He argued that while all deduction ultimately depends in one way or another on mental experimentation on schemata or diagrams, in corollarial deduction:
"it is only fundamental to imagine any issue in which the premises are true in lines to perceive immediately that the conclusion holds in that case"
while in theorematic deduction:
"It is necessary to experiment in the imagination upon the image of the premise in an arrangement of parts or elements in a specific produce figure or combination. from the sum of such(a) experiment to make corollarial deductions to the truth of the conclusion."
Peirce also held that corollarial deduction matches Aristotle's conception of direct demonstration, which Aristotle regarded as the only thoroughly satisfactory demonstration, while theorematic deduction is: