diff options
Diffstat (limited to 'src/Util/Fieldwise.v')
-rw-r--r-- | src/Util/Fieldwise.v | 42 |
1 files changed, 0 insertions, 42 deletions
diff --git a/src/Util/Fieldwise.v b/src/Util/Fieldwise.v deleted file mode 100644 index f2f0b5acb..000000000 --- a/src/Util/Fieldwise.v +++ /dev/null @@ -1,42 +0,0 @@ -Require Import Coq.Classes.Morphisms. -Require Import Relation_Definitions. - -Fixpoint tuple' n T : Type := - match n with - | O => T - | S n' => (tuple' n' T * T)%type - end. - -Definition tuple n T : Type := - match n with - | O => unit - | S n' => tuple' n' T - end. - -Fixpoint fieldwise' {A B} (n:nat) (R:A->B->Prop) (a:tuple' n A) (b:tuple' n B) {struct n} : Prop. - destruct n; simpl @tuple' in *. - { exact (R a b). } - { exact (R (snd a) (snd b) /\ fieldwise' _ _ n R (fst a) (fst b)). } -Defined. - -Definition fieldwise {A B} (n:nat) (R:A->B->Prop) (a:tuple n A) (b:tuple n B) : Prop. - destruct n; simpl @tuple in *. - { exact True. } - { exact (fieldwise' _ R a b). } -Defined. - -Global Instance Equivalence_fieldwise' {A} {R:relation A} {R_equiv:Equivalence R} {n:nat}: - Equivalence (fieldwise' n R). -Proof. - induction n; [solve [auto]|]. - simpl; constructor; repeat intro; intuition eauto. -Qed. - -Global Instance Equivalence_fieldwise {A} {R:relation A} {R_equiv:Equivalence R} {n:nat}: - Equivalence (fieldwise n R). -Proof. - destruct n; (repeat constructor || apply Equivalence_fieldwise'). -Qed. - -Arguments fieldwise' {A B n} _ _ _. -Arguments fieldwise {A B n} _ _ _.
\ No newline at end of file |