diff --git a/theories/countable.v b/theories/countable.v index 567903ad8e945be3c9f851d2db19362a029781d1..9e3a47e51cb601dcc2c045b3316f61d41fdaeb2d 100644 --- a/theories/countable.v +++ b/theories/countable.v @@ -348,11 +348,11 @@ Fixpoint gen_tree_of_list {T} Lemma gen_tree_of_to_list {T} k l (t : gen_tree T) : gen_tree_of_list k (gen_tree_to_list t ++ l) = gen_tree_of_list (t :: k) l. Proof. - revert t k l; fix 1; intros [|n ts] k l; simpl; auto. + revert t k l; fix FIX 1; intros [|n ts] k l; simpl; auto. trans (gen_tree_of_list (reverse ts ++ k) ([inl (length ts, n)] ++ l)). - rewrite <-(assoc_L _). revert k. generalize ([inl (length ts, n)] ++ l). induction ts as [|t ts'' IH]; intros k ts'''; csimpl; auto. - rewrite reverse_cons, <-!(assoc_L _), gen_tree_of_to_list; simpl; auto. + rewrite reverse_cons, <-!(assoc_L _), FIX; simpl; auto. - simpl. by rewrite take_app_alt, drop_app_alt, reverse_involutive by (by rewrite reverse_length). Qed. diff --git a/theories/numbers.v b/theories/numbers.v index e80bb32032f61969e4e17a6828958a72729be19a..4be6c114086767c9e46dbadd0bbaf966a4a60225 100644 --- a/theories/numbers.v +++ b/theories/numbers.v @@ -48,11 +48,11 @@ Instance nat_le_pi: ∀ x y : nat, ProofIrrel (x ≤ y). Proof. assert (∀ x y (p : x ≤ y) y' (q : x ≤ y'), y = y' → eq_dep nat (le x) y p y' q) as aux. - { fix 3. intros x ? [|y p] ? [|y' q]. + { fix FIX 3. intros x ? [|y p] ? [|y' q]. - done. - - clear nat_le_pi. intros; exfalso; auto with lia. - - clear nat_le_pi. intros; exfalso; auto with lia. - - injection 1. intros Hy. by case (nat_le_pi x y p y' q Hy). } + - clear FIX. intros; exfalso; auto with lia. + - clear FIX. intros; exfalso; auto with lia. + - injection 1. intros Hy. by case (FIX x y p y' q Hy). } intros x y p q. by apply (Eqdep_dec.eq_dep_eq_dec (λ x y, decide (x = y))), aux. Qed. diff --git a/theories/pretty.v b/theories/pretty.v index a26e574b794112f9ba097590afb559625fb7ea27..c879e43e4bdeefb604eeb1febce0accf41bb9408 100644 --- a/theories/pretty.v +++ b/theories/pretty.v @@ -25,7 +25,7 @@ Proof. done. Qed. Lemma pretty_N_go_help_irrel x acc1 acc2 s : pretty_N_go_help x acc1 s = pretty_N_go_help x acc2 s. Proof. - revert x acc1 acc2 s; fix 2; intros x [acc1] [acc2] s; simpl. + revert x acc1 acc2 s; fix FIX 2; intros x [acc1] [acc2] s; simpl. destruct (decide (0 < x)%N); auto. Qed. Lemma pretty_N_go_step x s : diff --git a/theories/relations.v b/theories/relations.v index d9e65e5da1064d7d1f345e3a36e0a825a7e9b8ce..fa27e104c6c741ae2424f54505d0b1186d6b3d2d 100644 --- a/theories/relations.v +++ b/theories/relations.v @@ -223,7 +223,7 @@ Lemma Fix_F_proper `{R : relation A} (B : A → Type) (E : ∀ x, relation (B x) (∀ y Hy Hy', E _ (f y Hy) (g y Hy')) → E _ (F x f) (F x g)) (x : A) (acc1 acc2 : Acc R x) : E _ (Fix_F B F acc1) (Fix_F B F acc2). -Proof. revert x acc1 acc2. fix 2. intros x [acc1] [acc2]; simpl; auto. Qed. +Proof. revert x acc1 acc2. fix FIX 2. intros x [acc1] [acc2]; simpl; auto. Qed. Lemma Fix_unfold_rel `{R: relation A} (wfR: wf R) (B: A → Type) (E: ∀ x, relation (B x)) (F: ∀ x, (∀ y, R y x → B y) → B x) diff --git a/theories/streams.v b/theories/streams.v index 0a1be8b6ea16a4566382ee7edaea6d7961c4403d..d4e610d50d3d266b8c0b0c9bc1fcf84e92538907 100644 --- a/theories/streams.v +++ b/theories/streams.v @@ -41,9 +41,9 @@ Proof. by constructor. Qed. Global Instance equal_equivalence : Equivalence (≡@{stream A}). Proof. split. - - now cofix; intros [??]; constructor. - - now cofix; intros ?? [??]; constructor. - - cofix; intros ??? [??] [??]; constructor; etrans; eauto. + - now cofix FIX; intros [??]; constructor. + - now cofix FIX; intros ?? [??]; constructor. + - cofix FIX; intros ??? [??] [??]; constructor; etrans; eauto. Qed. Global Instance scons_proper x : Proper ((≡) ==> (≡)) (scons x). Proof. by constructor. Qed. diff --git a/theories/stringmap.v b/theories/stringmap.v index eb6871db9b48ec00f917ec422e7afe2c44e6d96e..14fffc9671751490e9d484267e0ac3202a18de78 100644 --- a/theories/stringmap.v +++ b/theories/stringmap.v @@ -45,7 +45,7 @@ Lemma fresh_string_fresh {A} (m : stringmap A) s : m !! fresh_string s m = None. Proof. unfold fresh_string. destruct (m !! s) as [a|] eqn:Hs; [clear a Hs|done]. generalize 0 (wf_guard 32 (fresh_string_R_wf s m) 0); revert m. - fix 3; intros m n [?]; simpl; unfold fresh_string_go at 1; simpl. + fix FIX 3; intros m n [?]; simpl; unfold fresh_string_go at 1; simpl. destruct (Some_dec (m !! _)) as [[??]|?]; auto. Qed. Definition fresh_string_of_set (s : string) (X : stringset) : string :=