Proof: Do Control Map At Unchanged 28

Let's prove the following theorem:

if the following are true:

expression state at time 28 = "return"
Control Map at time 28 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 29 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given

1	expression state at time 28 = "return"
2	Control Map at time 28 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof Table

#	Claim	Reason
1	Control Map at time (28 + 1) = Control Map at time 28	if expression state at time 28 = "return", then Control Map at time (28 + 1) = Control Map at time 28 (Return (10))
2	Control Map at time (28 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (28 + 1) = Control Map at time 28 and Control Map at time 28 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (28 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality)
3	28 + 1 = 29	28 + 1 = 29 (Fixed Value Statement)
4	Control Map at time (28 + 1) = Control Map at time 29	if 28 + 1 = 29, then Control Map at time (28 + 1) = Control Map at time 29 (Substitution)
5	Control Map at time 29 = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (28 + 1) = Control Map at time 29 and Control Map at time (28 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 29 = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality Variation 2)

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