∀

logic.quest

Quaerere est invenire — To seek is to find.

↓ descend into the proof
∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥ ∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥
P1
I Premise

The Foundation of Inquiry

1. ∀x(P(x) → Q(x)) Axiom
2. P(a) Given

Every question worth pursuing begins with a single, irreducible assumption — a truth so fundamental it needs no proof, only the courage to state it.

∃ → ¬
∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥ ∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥
P2
II Premise

The Rules of Derivation

3. P(a) → Q(a) ∀-elim, 1
4. Q(a) →-elim, 2, 3

From axioms, through the machinery of inference, new truths emerge — not created, but revealed, as if they had always been waiting beneath the surface of reason.

∧ ∨ ⊢
∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥ ∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥
P3
III Premise

The Weight of Contradiction

5. ¬Q(a) → ⊥ Reductio
6. ∴ Q(a) ⊥-elim, 5

A contradiction is not a failure — it is the universe telling you that your assumptions have collided with truth. Listen carefully, and the path corrects itself.

⊥ ≡ ∀
∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥ ∴ ∵ ⊢ ⊣ ∧ ∨ ¬ → ↔ ∀ ∃ ⊥
Theorem

The Quest is the Proof

∀x(Quest(x) → Knowledge(x))

Every genuine quest — pursued with rigor, humility, and an unbroken chain of reasoning — arrives at knowledge. Not as a destination, but as the inevitable consequence of the journey itself.

■

Quod Erat Demonstrandum

logic.quest

The proof is complete. The quest continues.