chore: add regression test for issue 5925

The issue 5925 was closed with strong evidence that leanprover#6414 fixed the issue, and @mik-jozef kindly re-minimized their code that fails on 4.15.0-rc1 and found that it indeed works on the currently nightly for 4.16. This PR adds that as a regression test.

Author: kmill

Diff for: tests/lean/run/5925.lean

@@ -0,0 +1,65 @@
+/-!
+# Regression test for issue 5925
+https://github.com/leanprover/lean4/issues/5925
+
+This test was provided by @mik-jozef as an example that failed in v4.15.0-rc1 but is OK as of a nightly for 4.16.
+It is possible that this is the same issue as the one originally reported, but we have not checked.
+
+A difficulty is that the original reported example does not typecheck due to other fixes (#6024).
+We ought to verify that https://github.com/leanprover/lean4/pull/6414 indeed is the reason that the test in this file passes.
+-/
+
+def Set (D: Type) := D → Prop
+
+structure ValVar where
+  d: Empty
+  x: Nat
+
+structure Salgebra where
+  D: Type
+  I: Empty → Empty
+
+def pairSalgebra: Salgebra := ⟨Empty, nofun⟩
+
+structure Cause (D: Type) where
+  contextIns: Set Nat
+
+mutual
+inductive Ins (salg: Salgebra): Prop
+
+inductive IsCauseInapplicable (salg: Salgebra):
+  Cause salg.D → Prop
+
+| blockedContextIns
+  (cause: Cause salg.D)
+  (inContextIns: cause.contextIns 0)
+:
+  IsCauseInapplicable salg cause
+end
+
+def IsVarFree (x: Nat): Prop := ∀ d, ValVar.mk d x ∉ []
+
+def extOfIntCause
+  (internalCause: Cause Empty)
+:
+  Cause Empty
+:= {
+  contextIns :=
+    fun _ => ∃ vvI, internalCause.contextIns vvI ∧ IsVarFree vvI
+}
+
+def insInternalToInsExternal
+  (isInapp: IsCauseInapplicable pairSalgebra internalCause)
+:
+  IsCauseInapplicable pairSalgebra (extOfIntCause internalCause)
+:=
+  isInapp.rec
+    (motive_1 := fun _ => True)
+    (motive_2 :=
+      fun cause _ =>
+        IsCauseInapplicable pairSalgebra (extOfIntCause cause))
+    (fun cause inCins =>
+      IsCauseInapplicable.blockedContextIns
+        (salg := pairSalgebra)
+        (extOfIntCause cause)
+        (⟨_, inCins, nofun⟩))