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method AssignmentsToMark(students:int, tutors: int) returns (r:int)
requires students > 0 && tutors > 1
ensures r < students
{
assert students > 0 && tutors > 1;
assert students > 0 && tutors > 1 && true;
assert students > 0 && tutors > 1 && students/tutors < students ==> students/tutors < students;
DivisionLemma(students,tutors);
assert students/tutors < students;
r:= students/tutors;
assert r< students;
calc {
//true;
1/tutors < 1;
students/tutors < students;
}
lemma DivisionLemma(n:int,d:int)
requires n > 0 && d>1
ensures n/d < n
method AssignmentsToMarkOne(students:int, tutors: int) returns (r:int)
calc == {
true;
lemma CommonElement(a:array<nat>, b:array<nat>)
requires a.Length> 0 && b.Length > 0 && a[0] == b[0]
ensures multiset(a[..]) * multiset(b[..]) == multiset([a[0]]) + multiset(a[1..]) * multiset(b[1..])
//ensures multiset{a[..]} * multiset{b[..]} == multiset([a[0]]) + multiset{a[1..]} * multiset{b[1..]}
/*
var E := multiset{a[0]};
calc =={
multiset(a[..]) * multiset(b[..]);
assert (a[..] == [a[0]] + a[1..]) && (b[..] == [b[0]] + b[1..]);
(E+ multiset(a[1..])) * (E + multiset(a[1..]));
E + multiset(a[1..]) * multiset(b[1..]);
}*/