Proof: Do Control Map At Unchanged 42

Let's prove the following theorem:

if the following are true:
  • expression state at time 42 = "return"
  • Control Map at time 42 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 43 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 expression state at time 42 = "return"
2 Control Map at time 42 = [ entry 0: (pair ("while", 2)), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (42 + 1) = Control Map at time 42 if expression state at time 42 = "return", then Control Map at time (42 + 1) = Control Map at time 42
2 Control Map at time (42 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (42 + 1) = Control Map at time 42 and Control Map at time 42 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (42 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
3 42 + 1 = 43 42 + 1 = 43
4 Control Map at time (42 + 1) = Control Map at time 43 if 42 + 1 = 43, then Control Map at time (42 + 1) = Control Map at time 43
5 Control Map at time 43 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (42 + 1) = Control Map at time 43 and Control Map at time (42 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 43 = [ entry 0: (pair ("while", 2)), [ ] ]

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