Theorem 3.12: eventually coinciding sequences have coinciding limits

Proved

CogCons.coincide_limits_of_eventually_coincide

by Lucas · Sep 30, 2026 · Mathlib 0df444a (Lean v4.33.1)

consequence-operatorlogictopology

Let $(x_i)$ and $(y_i)$ be sequences of thoughts with $x_i \approx y_i$ for all $i \ge k$ . If $(x_i)$ converges to $x$ and $(y_i)$ converges to $y$ , then $x \approx y$ .

Preamble

import Mathlib
import Definitions.Def_CogCons_similarity_distance

open CogCons.CognitiveSimilarityDistance

Formal statement

namespace CogCons

theorem coincide_limits_of_eventually_coincide {C : Type*} (D : CognitiveSimilarityDistance C)
    (s t : ℕ → C) (k : ℕ) (hst : ∀ i ≥ k, D.coincide (s i) (t i))
    (x y : C) (hs : D.ConvergesTo s x) (ht : D.ConvergesTo t y) :
    D.coincide x y := by sorry

end CogCons

Source

S. Acharjee and U. Gogoi, *The limit of human intelligence*, arXiv:2310.10792v2 [math.GM] (2023), https://arxiv.org/abs/2310.10792, Theorem 3.12 (p. 15)

Read-back

What the Lean code literally says, in plain math · Aristotle (Harmonic)

Non-blind read-back — not independent testimony. This read-back was written by the same agent that drafted these Lean statements, not by an independent auditor working blind from the code alone. The author knew the intended meaning while writing it, so it may read that intent into the code. Do not treat it as independent verification; compare the Lean code against the source directly.

For every type $C$ , every cognitive similarity distance $D$ on $C$ (as above), all sequences $s, t : \mathbb N \to C$ and every $k \in \mathbb N$ with $s_i \approx t_i$ for all $i \ge k$ , and all $x, y \in C$ : if $s$ converges to $x$ and $t$ converges to $y$ (for every $\varepsilon \in (0,1)$ , $\mathrm{Cog}(x, s_n) < \varepsilon$ eventually, resp. $\mathrm{Cog}(y, t_n) < \varepsilon$ eventually), then $x \approx y$ .

Human review

Endorsed by Shuze Chen · Sep 30, 2026
Confirmed by the moderator at approval.
Endorsed by Lucas · Sep 30, 2026
Confirmed by the mission captain (proposal self-audit).

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