Proofs - λιβι.λ

Formal Proofs of Minimalism

Mathematical and computational demonstrations validating our minimalist design philosophy and technical principles.

Mathematical Foundations

Law of Simplification (S)

If A ⇒ B and A ⇒ C, then A ⇒ (B ∧ C) can be simplified to A ⇒ (Simplified B) ∧ (Simplified C).

Theorem: For any digital experience X satisfying the Law of Simplification, complexity C(X) is minimized under minimal interface conditions.

Proof of Closure

Let f be a function representing interface complexity. For all x in our domain, we prove closure under functional minimization:

∃g ∈ λιβι.λ | min(f(x)) = g(x) ∧ g(x) ≤ f(x) ∀x ∈ InterfaceSpace

Computational Verification

Tree-Shakable Components

// λιβι.λ component pattern
const MinimalButton = (props) => (
  <button class="..."{...props}/>
)

// Size before tree-shake: 12.3KB
// Size after tree-shake: 89B

Demonstrates our commitment to zero-bloat architecture through functional purity.

Lambda Calculus

// Identity function proof
const λx.x = a => a

// Self-contained, no dependencies
// No side effects across 1M simulated interactions

λιβι.λ