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+-- I actually thought that ∀p, ∃q, (q ≠ p) ∧ q!
+-- However, propositional extensionality tells us that (p ↔ q) → p = q
+
+theorem finiteTrueProps
+    : ¬∀p, ∃q, (q ≠ p) ∧ q := by
+  intro h
+  have := h True
+  simp at this
+
+theorem finiteFalseProps
+    : ¬∀p, ∃q, (q ≠ p) ∧ ¬q := by
+  intro h
+  have := h False
+  simp at this