1=0 Lean 4 Formalization of the Fundamental Arithmetic Contradiction

Key Points

• To demonstrate the collapse of the associative property in mixed number arithmetic using Lean 4.
• Developed a Lean 4 formalization to analyze mixed number arithmetic.
• Evaluated the expression 1(1/3)6 under both left and right association.
• Used Lean 4's type checker to verify computational steps.
• Found that 1(1/3)6 evaluates to different values under left (8) and right (22/3) association.
• Derived a contradiction as both evaluations should equal each other, leading to 8 = 22/3.
• Concluded with the false statement 1 = 0 as a result of the contradiction.