[tlaplus] simple toy theorem

[jack malkovick <sillymouse333@xxxxxxxxx>]

Let's say we have this simple theorem

THEOREM T ==
    ASSUME
        NEW NEW S(_), NEW U(_), NEW M(_), NEW P(_),
        \A x : M(x) = S(x) /\ ~U(x),
        \A x : P(x) = M(x)
   PROVE
        \A x : P(x) => S(x)

   PROOF
        OBVIOUS

It is true.

If I negate the goal to \E x : ~(P(x) => S(x)) same as \E x : P(x) /\ ~S(x) it becomes red.

However, if I add another assumption
NEW B(_), \A x : B(x) = S(x) /\ U(x),

The theorem turns green! How can this new assumption make the theorem true?

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