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+(* On the strength of "apply with" (see also #4782) *)
+
+Record ProverT := { Facts : Type }.
+Record ProverT_correct (P : ProverT) := { Valid : Facts P -> Prop ;
+ Valid_weaken : Valid = Valid }.
+Definition reflexivityValid (_ : unit) := True.
+Definition reflexivityProver_correct : ProverT_correct {| Facts := unit |}.
+Proof.
+ eapply Build_ProverT_correct with (Valid := reflexivityValid).