Commit 52cc6b15 authored by Ralf Jung's avatar Ralf Jung
Browse files

slightly simplify some proofs in upred.v

parent 3a86d2ff
...@@ -341,13 +341,13 @@ Global Instance iff_proper : ...@@ -341,13 +341,13 @@ Global Instance iff_proper :
(** Introduction and elimination rules *) (** Introduction and elimination rules *)
Lemma const_intro φ P : φ P φ. Lemma const_intro φ P : φ P φ.
Proof. by intros ?? [|?]. Qed. Proof. by intros ???. Qed.
Lemma const_elim φ Q R : Q φ (φ Q R) Q R. Lemma const_elim φ Q R : Q φ (φ Q R) Q R.
Proof. intros HQP HQR x n ??; apply HQR; first eapply (HQP _ n); eauto. Qed. Proof. intros HQP HQR x n ??; apply HQR; first eapply (HQP _ n); eauto. Qed.
Lemma True_intro P : P True. Lemma True_intro P : P True.
Proof. by apply const_intro. Qed. Proof. by apply const_intro. Qed.
Lemma False_elim P : False P. Lemma False_elim P : False P.
Proof. by intros x [|n] ?. Qed. Proof. by intros x n ?. Qed.
Lemma and_elim_l P Q : (P Q) P. Lemma and_elim_l P Q : (P Q) P.
Proof. by intros x n ? [??]. Qed. Proof. by intros x n ? [??]. Qed.
Lemma and_elim_r P Q : (P Q) Q. Lemma and_elim_r P Q : (P Q) Q.
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment