Changes

==Case analysis-synthesis theorem==

==Case analysis-synthesis theorem==

The substance of this principle was known to Boole a sesquicentury ago, tantamount to the ''Boolean Expansion'' that he uncovered while nameless.  So the only novelty here will rest in a certain manner of presentation, in which I will prove the basic principle from the axioms given before.  One name for this rule is the ''Case Analysis-Synthesis Theorem'' (CAST).

The task at hand is build a bridge between model-theoretic and proof-theoretic perspectives on logical procedure, though for now we join them at a point so close to their common source that it may not seem worth the candle at all.  The substance of this principle was known to Boole a sesquicentury ago, tantamount to the ''boolean expansion'' that he uncovered while nameless.  So the only novelty here will rest in a certain manner of presentation, in which I will prove the basic principle from the axioms given before.  One name for this rule is the ''Case Analysis-Synthesis Theorem'' (CAST).

The preparatory materials that we need are these:

The preparatory materials that we need are these:

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Nota Bene.  QES = Quod Erat Sketchiendum.

===Example===

Some of the jobs that the CAST can be usefully put to work on are proving propositional theorems and establishing equations between propositions.  Once again, let us turn to the example of Leibniz's Praeclarum Theorema as a way of illustrating how.  It will suffice to work within the Existential interpretation.

Some of the jobs that the CAST can be usefully put to work on are proving propositional theorems and establishing equations between propositions.  Once again, let us turn to the example of Leibniz's Praeclarum Theorema as a way of illustrating how.  It will suffice to work within the Existential interpretation.