Proof: Do Variables At Unchanged 81

Let's prove the following theorem:

if the following are true:

expression state at time 81 = "call_returned"
Variables Map at time 81 = [ entry joe: (Python reference 0), [ ] ]

then Variables Map at time 82 = [ entry joe: (Python reference 0), [ ] ]

Proof:

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Given

1	expression state at time 81 = "call_returned"
2	Variables Map at time 81 = [ entry joe: (Python reference 0), [ ] ]

Proof Table

#	Claim	Reason
1	Variables Map at time (81 + 1) = Variables Map at time 81	if expression state at time 81 = "call_returned", then Variables Map at time (81 + 1) = Variables Map at time 81 (Call Returned Unchanged (1))
2	Variables Map at time (81 + 1) = [ entry joe: (Python reference 0), [ ] ]	if Variables Map at time (81 + 1) = Variables Map at time 81 and Variables Map at time 81 = [ entry joe: (Python reference 0), [ ] ], then Variables Map at time (81 + 1) = [ entry joe: (Python reference 0), [ ] ] (Transitive Property of Equality)
3	81 + 1 = 82	81 + 1 = 82 (Fixed Value Statement)
4	Variables Map at time (81 + 1) = Variables Map at time 82	if 81 + 1 = 82, then Variables Map at time (81 + 1) = Variables Map at time 82 (Substitution)
5	Variables Map at time 82 = [ entry joe: (Python reference 0), [ ] ]	if Variables Map at time (81 + 1) = Variables Map at time 82 and Variables Map at time (81 + 1) = [ entry joe: (Python reference 0), [ ] ], then Variables Map at time 82 = [ entry joe: (Python reference 0), [ ] ] (Transitive Property of Equality Variation 2)

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