Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
The lemma `exists_const` already handles all real cases of `(∃ _ : α, p) ↔ p` for general types `α`. If there are no `Nonempty` instances and this lemma cannot apply, it seems unlikely that simp could make more progress with `(∃ _ : α, p) ↔ Nonempty α ∧ p`. However, it is still worth simplifying `(∃ _ : p, q)` to `p ∧ q`. Also adds a `Nonempty (Decidable a)` instance, which is used by Mathlib. |
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