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// RUN: %dafny /compile:3 /print:"%t.print" /dprint:"%t.dprint" "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
method Main()
{
test0(10);
test5(11);
test6(12);
test1();
test2();
}
predicate valid(x:int)
{
x > 0
}
function ref1(y:int) : int
requires valid(y);
{
y - 1
}
lemma assumption1()
ensures forall a, b :: valid(a) && valid(b) && ref1(a) == ref1(b) ==> a == b;
{
}
method test0(a: int)
{
if ref1.requires(a) {
// the precondition should suffice to let us call the method
ghost var b := ref1(a);
}
}
method test5(a: int)
{
if valid(a) {
// valid(a) is the precondition of ref1
assert ref1.requires(a);
}
}
method test6(a: int)
{
if ref1.requires(a) {
// the precondition of ref1 is valid(a)
assert valid(a);
}
}
method test1()
{
if * {
assert forall a, b :: valid(a) && valid(b) && ref1(a) == ref1(b) ==> a == b;
} else {
assert forall a, b :: ref1.requires(a) && ref1.requires(b) && ref1(a) == ref1(b)
==> a == b;
}
}
function {:opaque} ref2(y:int) : int // Now with an opaque attribute
requires valid(y);
{
y - 1
}
lemma assumption2()
ensures forall a, b :: valid(a) && valid(b) && ref2(a) == ref2(b) ==> a == b;
{
reveal_ref2();
}
method test2()
{
assumption2();
if * {
assert forall a, b :: valid(a) && valid(b) && ref2(a) == ref2(b) ==> a == b;
} else {
assert forall a, b :: ref2.requires(a) && ref2.requires(b) && ref2(a) == ref2(b)
==> a == b;
}
}
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