Proof: Do Variables At Unchanged 22

Let's prove the following theorem:

if the following are true:

expression state at time 22 = "call_function_begin"
Variables Map at time 22 = [ ]

then Variables Map at time 23 = [ ]

Proof:

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Given

1	expression state at time 22 = "call_function_begin"
2	Variables Map at time 22 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (22 + 1) = Variables Map at time 22	if expression state at time 22 = "call_function_begin", then Variables Map at time (22 + 1) = Variables Map at time 22 (Assign Parent (5))
2	Variables Map at time (22 + 1) = [ ]	if Variables Map at time (22 + 1) = Variables Map at time 22 and Variables Map at time 22 = [ ], then Variables Map at time (22 + 1) = [ ] (Transitive Property of Equality)
3	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
4	Variables Map at time (22 + 1) = Variables Map at time 23	if 22 + 1 = 23, then Variables Map at time (22 + 1) = Variables Map at time 23 (Substitution)
5	Variables Map at time 23 = [ ]	if Variables Map at time (22 + 1) = Variables Map at time 23 and Variables Map at time (22 + 1) = [ ], then Variables Map at time 23 = [ ] (Transitive Property of Equality Variation 2)

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