[tlaplus] meaning of the lead to (~>) operator

[seup yun <syun4541@xxxxxxxxx>]

Hi,

I'm trying to specify "If some operation does not happens, then some condition eventually becomes true"

full specification is following:

-------------------------------- MODULE test --------------------------------

EXTENDS Integers

VARIABLE x,y

Init ==
    /\ x = 0
    /\ y = 0

IncX ==
    /\ x' = IF x < 5 THEN (x + 1) ELSE 5
    /\ UNCHANGED <<y>>

IncY ==
    /\ x > 0
    /\ y' = IF y < 5 THEN (y + 1) ELSE 5
    /\ UNCHANGED <<x>>

SetX ==
    /\ x' = -1
    /\ UNCHANGED <<y>>

Next ==
    \/ IncX
    \/ IncY
    \/ SetX
    
Invariant1 ==
    /\ x < 6
    /\ y < 6
    
temporalFormula1 ==  (x > 0) ~> (y = 5)
=============================================================================

and behavior spec is:

Init /\ [][Next]_<<x,y>> /\ WF_x(IncX) /\ WF_x(SetX) /\ WF_<<x,y>>(IncY)

my question is, why temporalFormula1 is violated?

I know that (x > 0) ~> (y = 5) means:

□((x > 0) => <>(y = 5)) which is

\A n \in Nat. \sigma^{+n} ⊨ (x > 0) => ¬□¬(y = 5) which is

\A n \in Nat. \sigma^{+n} ⊨ (x > 0) => \sigma^{+n} ⊨ \E m \in Nat. \sigma{+m} ⊨ (y = 5) which is

\A n \in Nat. \sigma^{+n} ⊨ (x > 0) => \E m \in Nat. \sigma^{+n+m} ⊨ (y = 5)

so, i believed that error-trace should not contains the state that x is -1 but it does. 

I even tried the formula (FALSE) ~> (y = 5) but it still fails with similar error trace. what's my mistake here?

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