Proof: Do Variables At Unchanged 51

Let's prove the following theorem:

if the following are true:

expression state at time 51 = "call_returned"
Variables Map at time 51 = [ ]

then Variables Map at time 52 = [ ]

Proof:

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Given

1	expression state at time 51 = "call_returned"
2	Variables Map at time 51 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (51 + 1) = Variables Map at time 51	if expression state at time 51 = "call_returned", then Variables Map at time (51 + 1) = Variables Map at time 51 (Call Returned Unchanged (1))
2	Variables Map at time (51 + 1) = [ ]	if Variables Map at time (51 + 1) = Variables Map at time 51 and Variables Map at time 51 = [ ], then Variables Map at time (51 + 1) = [ ] (Transitive Property of Equality)
3	51 + 1 = 52	51 + 1 = 52 (Fixed Value Statement)
4	Variables Map at time (51 + 1) = Variables Map at time 52	if 51 + 1 = 52, then Variables Map at time (51 + 1) = Variables Map at time 52 (Substitution)
5	Variables Map at time 52 = [ ]	if Variables Map at time (51 + 1) = Variables Map at time 52 and Variables Map at time (51 + 1) = [ ], then Variables Map at time 52 = [ ] (Transitive Property of Equality Variation 2)

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