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Diffstat (limited to 'theories/Arith/Between.v')
| -rw-r--r-- | theories/Arith/Between.v | 4 |
1 files changed, 4 insertions, 0 deletions
diff --git a/theories/Arith/Between.v b/theories/Arith/Between.v index 9b4071085..ead08b3eb 100644 --- a/theories/Arith/Between.v +++ b/theories/Arith/Between.v @@ -16,6 +16,8 @@ Implicit Types k l p q r : nat. Section Between. Variables P Q : nat -> Prop. + (** The [between] type expresses the concept + [forall i: nat, k <= i < l -> P i.]. *) Inductive between k : nat -> Prop := | bet_emp : between k k | bet_S : forall l, between k l -> P l -> between k (S l). @@ -47,6 +49,8 @@ Section Between. induction 1; auto with arith. Qed. + (** The [exists_between] type expresses the concept + [exists i: nat, k <= i < l /\ Q i]. *) Inductive exists_between k : nat -> Prop := | exists_S : forall l, exists_between k l -> exists_between k (S l) | exists_le : forall l, k <= l -> Q l -> exists_between k (S l). |