Proof: Do Variables At Unchanged 20

Let's prove the following theorem:

if the following are true:

expression state at time 20 = "call_function_begin"
Variables Map at time 20 = [ ]

then Variables Map at time 21 = [ ]

Proof:

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Given

1	expression state at time 20 = "call_function_begin"
2	Variables Map at time 20 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (20 + 1) = Variables Map at time 20	if expression state at time 20 = "call_function_begin", then Variables Map at time (20 + 1) = Variables Map at time 20 (Assign Parent (5))
2	Variables Map at time (20 + 1) = [ ]	if Variables Map at time (20 + 1) = Variables Map at time 20 and Variables Map at time 20 = [ ], then Variables Map at time (20 + 1) = [ ] (Transitive Property of Equality)
3	20 + 1 = 21	20 + 1 = 21 (Fixed Value Statement)
4	Variables Map at time (20 + 1) = Variables Map at time 21	if 20 + 1 = 21, then Variables Map at time (20 + 1) = Variables Map at time 21 (Substitution)
5	Variables Map at time 21 = [ ]	if Variables Map at time (20 + 1) = Variables Map at time 21 and Variables Map at time (20 + 1) = [ ], then Variables Map at time 21 = [ ] (Transitive Property of Equality Variation 2)

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