Java (JDK), 43 bytes
a->a.sorted().reduce(1,(x,y)->y==x?x+1:0)>0
Explanations
This answer is a Predicate<IntStream> and requires that the input contains no 0.
First this code sorts the input stream. The reduce method then makes sure that each consecutive number is encountered, and return the last encountered number. x always contains the next expected number, or 0 if we got an unexpected number. 1 is the first parameter of the reduce method as it's the first expected number. Given that 0, or any negative number, is not allowed in the IntStream, when 0 is returned for the first time, it will always be returned for the remaining of the process.
Java (JDK), 43 bytes
a->a.sorted().reduce(1,(x,y)->y==x?x+1:0)>0
Explanations
This answer is a Predicate<IntStream> and requires that the input contains no 0.
First this code sorts the input stream. The reduce method then makes sure that each consecutive number is encountered, and return the last encountered number. x always contains the next expected number, or 0 if we got an unexpected number. 1 is the first parameter of the reduce method as it's the first expected number. Given that 0, or any negative number, is not allowed in the IntStream, when 0 is returned for the first time, it will always be returned for the remaining of the process.
Java (JDK), 43 bytes
a->a.sorted().reduce(1,(x,y)->y==x?x+1:0)>0
Assumes a contains only strictly positive numbers.
Java (JDK), 43 bytes
a->a.sorted().reduce(1,(x,y)->y==x?x+1:0)>0
Assumes a contains only strictly positive numbers.