Lean Theorems

A repository dedicated to my journey learning and implementing theorems in Lean 4. This space serves as both a study log and implementation archive for various mathematical and philosophical theorems.

Repository Structure

• 📁 Studying/
  • 📁 Philosophical/
    • sri_yantra.lean - Implementation of Sri Yantra geometric properties and theorems using Lean 4

Current Projects

Sri Yantra Implementation Details

The Sri Yantra implementation focuses on formalizing sacred geometry using rigorous mathematical proofs in Lean 4.

Core Structures

• SriYantraTriangle: Represents the fundamental triangular structures with:

  • Equilateral triangle properties
  • Circumcenter calculations
  • Sacred proportion constraints
  • Angular relationships (2π sum constraint)

• ShaktiPath: Models the energy pathways with:

  • Continuous path properties
  • Start and end point definitions
  • Flow direction constraints
  • Energy flow angle calculations (0 ≤ θ ≤ 2π)

Key Theorems

1. Geometric Properties

• Golden Ratio relationships (φ = (1 + √5)/2)
• Sacred circle ratios (√3 relationship between circumradius and inradius)
• Angular relationships (π/6 relationships between triangles)

2. Pathway Analysis

• Intersection point properties (54 critical points)
• Bindu flow characteristics
• Mandala structure (9 centers and 9 radii)

3. Unified Properties The implementation proves a comprehensive theorem (sri_yantra_complete_properties) that unifies:

• Golden ratio relationships
• Sacred circle proportions
• Angular symmetries
• Pathway intersections
• Bindu flow properties
• Mandala structural relationships

Prerequisites

Core Requirements

• Lean 4
  • Installation of Lean 4 compiler
  • Basic understanding of Lean syntax
  • Experience with functional programming concepts

Library Dependencies

• Mathlib
  • Core mathematical libraries
  • Theorem proving foundations
  • Type theory basics

Mathematical Background

Required Knowledge:

• Euclidean Geometry

  • Geometric constructions
  • Triangle properties
  • Circle theorems
  • Vector spaces

• Metric Spaces

  • Distance functions
  • Convergence concepts
  • Completeness
  • Topology fundamentals

• Topology

  • Open and closed sets
  • Continuous functions
  • Connectedness
  • Compactness

• Real Analysis

  • Limit theory
  • Continuity
  • Differentiation
  • Integration theory

Future Plans

Mathematical Implementations

1. Philosophical Mathematics

   • Sacred geometry theorems
   • Number theory relationships
   • Geometric patterns in nature
   • Mathematical symmetry principles

2. Classical Theorems

   • Fundamental theorem of algebra
   • Prime number theorems
   • Group theory foundations
   • Topology fundamentals

Learning Track

1. Study Notes

   • Theorem proving techniques
   • Lean 4 best practices
   • Mathematical proof strategies
   • Code organization patterns

2. Progress Tracking

   • Implementation milestones
   • Theorem complexity progression
   • Learning achievements
   • Documentation improvements

Planned Features

• Comprehensive documentation
• Example collections
• Tutorial sections
• Reference implementations