Proof: Write Stmt Control Map At Unchanged 4

Let's prove the following theorem:

if the following are true:

the line at time 4 = 5
the tab at time 4 = 0
statement at line 5, tab 0 = b = add_three(a)
Control Map at time 4 = [ ]

then Control Map at time 5 = [ ]

Proof:

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Given

1	the line at time 4 = 5
2	the tab at time 4 = 0
3	statement at line 5, tab 0 = `b = add_three(a)`
4	Control Map at time 4 = [ ]

Proof Table

#	Claim	Reason
1	Control Map at time (4 + 1) = Control Map at time 4	if the line at time 4 = 5 and the tab at time 4 = 0 and statement at line 5, tab 0 = `b = add_three(a)`, then Control Map at time (4 + 1) = Control Map at time 4 (Assign If Stack (3))
2	Control Map at time (4 + 1) = [ ]	if Control Map at time (4 + 1) = Control Map at time 4 and Control Map at time 4 = [ ], then Control Map at time (4 + 1) = [ ] (Transitive Property of Equality)
3	4 + 1 = 5	4 + 1 = 5 (Fixed Value Statement)
4	Control Map at time (4 + 1) = Control Map at time 5	if 4 + 1 = 5, then Control Map at time (4 + 1) = Control Map at time 5 (Substitution)
5	Control Map at time 5 = [ ]	if Control Map at time (4 + 1) = Control Map at time 5 and Control Map at time (4 + 1) = [ ], then Control Map at time 5 = [ ] (Transitive Property of Equality Variation 2)

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