From 3f9948eaf921c46357665a35d49d5d9470787669 Mon Sep 17 00:00:00 2001
From: mehbark <terezi@pyrope.net>
Date: Tue, 8 Apr 2025 22:10:20 -0400
Subject: [PATCH] FinitudeOfPropositions

---
 SimpleCounterexamples/FinitudeOfPropositions.lean | 14 ++++++++++++++
 1 file changed, 14 insertions(+)
 create mode 100644 SimpleCounterexamples/FinitudeOfPropositions.lean

diff --git a/SimpleCounterexamples/FinitudeOfPropositions.lean b/SimpleCounterexamples/FinitudeOfPropositions.lean
new file mode 100644
index 0000000..12b8eb9
--- /dev/null
+++ b/SimpleCounterexamples/FinitudeOfPropositions.lean
@@ -0,0 +1,14 @@
+-- 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