Consensus.tla

----------------------------- MODULE Consensus ------------------------------
EXTENDS Integers, FiniteSets, Sets, TLAPS 
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CONSTANT Value  \* the set of values that can be chosen
VARIABLE chosen \* the set of values that have been chosen
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Init == chosen = {}

Next == 
    /\ chosen = {}
    /\ \E v \in Value : chosen' = {v}

Spec == Init /\ [][Next]_chosen
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Inv == 
    /\ chosen \subseteq Value
    /\ IsFiniteSet(chosen)
    /\ Cardinality(chosen) \leq 1
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THEOREM Invariance == Spec => []Inv
<1>1. Init => Inv
  BY CardinalityZero, SMT DEF Init, Inv
<1>2. Inv /\ [Next]_chosen => Inv'
  BY CardinalityOne, SMT DEF Next, Inv
<1>3. QED 
  BY <1>1, <1>2, PTL DEF Spec
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