valid

In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. P->Q Table

assert and check

In Alloy, fact is the premises, assert is the conclusion and check is to check the validity between the premises and the conclusion.

If the fact is false, check would always return valid. It will show,

No counterexample found. Assertion may be valid.

fact {
  1 = 2
}
assert any_assertion {
  1 = 2
  1 != 2
}
check  any_assertion

all

all a : A | =>