Theorem 3.3: some thought lies in no CWO set

Proved

CogCons.exists_not_mem_cwo

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

consequence-operatorlogictopology

In every cognitive-consequence space there is a mental representation $f \in C$ that belongs to no CWO set:

\exists f \in C\ \ \forall A \in \tau:\ f \notin A.

Preamble

import Mathlib
import Definitions.Def_CogCons_consequence_space

open CogCons.CognitiveConsequenceSpace

Formal statement

namespace CogCons

theorem exists_not_mem_cwo {C : Type*} (S : CognitiveConsequenceSpace C) :
    ∃ f : C, ∀ A : Set C, S.IsCWO A → f ∉ A := 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 3.3 (p. 7)

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 $C$ and every cognitive-consequence space $S$ on $C$ (countable $C$ ; $\mathrm{Cn}$ inclusive, monotone, idempotent, finitary; deduction property for $\Rightarrow$ ; $\mathrm{Cn}(\varnothing)$ nonempty), there exists $f \in C$ such that every $A \subseteq C$ with $\mathrm{Cn}(C \setminus A) = C \setminus A$ does not contain $f$ . The nonemptiness of $\mathrm{Cn}(\varnothing)$ is part of the structure; in particular $C$ is nonempty.

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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