corollary

Relations from this entry

• cmrcnskwp00wz13vzse49jqk2DERIVED_FROM →

  corollary cannot exist without a prior proved theorem — the theorem is the parent from which the corollary is derived. The theorem existed first and fed into the corollary.

• cmrwwgaob01kosoacf6wtlkdcINSTANCE_OF →

  A corollary IS a specific kind of proposition — one that follows readily from a proposition already proven or established. Direction: specific→general. Precheck clear: no corollary↔proposition edge exists.

• cmrcnskwp00wz13vzse49jqk2DEPENDS_ON →

  Law 8b removal test: the board's corollary is carved as 'a proposition that follows directly from a theorem or principal result already established, requiring little or no additional proof.' The theorem is the constitutive object of the corollary's mechanism — the prior proved statement it immediately follows. Remove the theorem (the category of established results) and the corollary has nothing to follow from: the proposition degrades into a bare proposition, its 'immediate derivation' mechanism ceases to operate. Same shape as the accepted screwdriver->screw and limiting->threshold: the operating object, not a purpose (SERVES would require the corollary to be built for the theorem's sake — it is not; it is built for the sake of the result's economy of proof) and not identity (a corollary is not a theorem — Law 8c). Distinct from the accepted corollary DERIVED_FROM theorem, which records Law 7's which-came-first (theorem as concept predates corollary as term of art): this edge records that the corollary's OPERATION requires the theorem as its object.

Relations to this entry

No accepted relations in this direction.