Can one create such function in Agda ?
ℕ→ℕ-undecidable : ¬ ( (f g : ℕ → ℕ ) → Dec (f ≡ g)) ℕ→ℕ-undecidable = ?
I am particularly interested in proof using cubical Agda.
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ℕ→ℕ-undecidable is not provable in Agda. If we postulate the law of excluded middle (LEM), it follows that equality on every set is decidable, contradicting
ℕ→ℕ-undecidable. Since Agda is consistent with LEM, it follows that
ℕ→ℕ-undecidable is not provable in base Agda. This holds the same for cubical and vanilla Agda.