Proof: Do Control Map At Unchanged 2

Let's prove the following theorem:

if the following are true:

expression state at time 2 = "iterate_args"
Control Map at time 2 = [ ]

then Control Map at time 3 = [ ]

Proof:

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Given

1	expression state at time 2 = "iterate_args"
2	Control Map at time 2 = [ ]

Proof Table

#	Claim	Reason
1	Control Map at time (2 + 1) = Control Map at time 2	if expression state at time 2 = "iterate_args", then Control Map at time (2 + 1) = Control Map at time 2 (Iterate Insn (7))
2	Control Map at time (2 + 1) = [ ]	if Control Map at time (2 + 1) = Control Map at time 2 and Control Map at time 2 = [ ], then Control Map at time (2 + 1) = [ ] (Transitive Property of Equality)
3	2 + 1 = 3	2 + 1 = 3 (Fixed Value Statement)
4	Control Map at time (2 + 1) = Control Map at time 3	if 2 + 1 = 3, then Control Map at time (2 + 1) = Control Map at time 3 (Substitution)
5	Control Map at time 3 = [ ]	if Control Map at time (2 + 1) = Control Map at time 3 and Control Map at time (2 + 1) = [ ], then Control Map at time 3 = [ ] (Transitive Property of Equality Variation 2)

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