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Structural ·2026-06-21 00:00 UTC

Addition of natural numbers is commutative

Structural ·arithmetic and number theory ·specimen

Enuntiatio — the claim

Addition of natural numbers is commutative

Refuted by two naturals a, b with a + b ≠ b + a

Expressio — the formal statement

import Mathlib.Tactic

theorem add_comm_nat (a b : Nat) : a + b = b + a

Demonstratio — the kernel-checked proof

by ring
Q.E.D. kernel verified: true
Monas — the indivisible unity