Simple Assertion for Counter

Hi all, 

Question_1 : Assertion requirement :

When Enable is HIGH, counter should be increment to previous clock cycle value, when Enable is LOW, counter should keep same value as previous cycle.

Below is my understanding. May I know is this satisfying the requirement or require changes?

property p1;

@(posedge clk) Enable |=> (count == $past(count+1));

endproperty

Question_2 : also, do we require one more property for else condition. Like

property p2;

@(posedge clk) (!Enable) |=> (count == $past(count));

endproperty

Is only one property (p1) is sufficient for above requirement.

Kindly suggest