Armed with Theory
Every argument begins with an unshakeable foundation. The premise is the bedrock upon which all subsequent reasoning is constructed — immovable, precise, absolute.
From axioms, we derive truths through chains of inference. Each step follows necessarily from the last — no gaps, no leaps of faith, only crystalline logic.
The theorem stands as proof of the system's integrity. It is both weapon and shield — an intellectual construct so rigorous it withstands all assault.
What follows from the proven theorem extends the armor further. Each corollary is another plate of defense, another edge of the blade.
If P implies Q, and P is true, then Q is necessarily true. The fundamental rule of detachment — the simplest weapon in the logical arsenal.
P → Q, P ⊢ Q
Assume the negation; derive a contradiction. The elegant destroyer — turning the enemy's position against itself through its own internal inconsistency.
¬P → ⊥ ⊢ P
What holds for the arbitrary holds for all. The leap from particular to universal — the most powerful expansion of theoretical armor.
P(a) ⊢ ∀x P(x)