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Polymorphic Axiom inhabited@{u} : Type@{u} -> Prop.
Polymorphic Axiom unit@{u} : Type@{u}.
Polymorphic Axiom tt@{u} : inhabited unit@{u}.
#[export] Polymorphic Hint Resolve tt : the_lemmas.
Set Printing All.
Set Printing Universes.
Goal inhabited unit.
Proof.
eauto with the_lemmas.
Qed.
Universe u.
Axiom f : Type@{u} -> Prop.
Lemma fapp (X : Type) : f X -> False.
Admitted.
Polymorphic Axiom funi@{i} : f unit@{i}.
Goal (forall U, f U) -> (*(f unit -> False) -> *)False /\ False.
pose (H := fapp unit funi).
eauto using H. (* The two fapp's have different universes *)
Qed.
Definition fapp0 := fapp unit funi.
#[export] Hint Resolve fapp0 : mylems.
Goal (forall U, f U) -> (*(f unit -> False) -> *)False /\ False.
eauto with mylems. (* Forces the two fapps at the same level *)
Qed.
Goal (forall U, f U) -> (f unit -> False) -> False /\ False.
eauto. (* Forces the two fapps at the same level *)
Qed.
Polymorphic Definition MyType@{i} := Type@{i}.
Universes l m n.
Constraint l < m.
Polymorphic Axiom maketype@{i} : MyType@{i}.
Goal MyType@{l}.
Proof.
Fail solve [ pose (mk := maketype@{m}); eauto using mk ].
eauto using maketype.
Undo.
pose (mk := maketype@{n}); eauto using mk.
Qed.
Axiom foo : forall (A : Type), list A.
Polymorphic Axiom foop@{i} : forall (A : Type@{i}), list A.
Universe x y.
Goal list Type@{x}.
Proof.
pose (H := foo Type); eauto using H. (* Refreshes the term *)
Undo.
eauto using foo. Show Universes.
Undo.
eauto using foop. Show Proof. Show Universes.
Qed.
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