Proof: Write Stmt Control Map At Unchanged 3

Let's prove the following theorem:

if the following are true:

the line at time 3 = 4
the tab at time 3 = 0
statement at line 4, tab 0 = a = 5
Control Map at time 3 = [ ]

then Control Map at time 4 = [ ]

Proof:

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Given

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

Proof Table

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

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