Proof: Do Control Map At Unchanged 37

Let's prove the following theorem:

if the following are true:
  • expression state at time 37 = "iterate_args"
  • Control Map at time 37 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 38 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 expression state at time 37 = "iterate_args"
2 Control Map at time 37 = [ entry 0: (pair ("while", 2)), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (37 + 1) = Control Map at time 37 if expression state at time 37 = "iterate_args", then Control Map at time (37 + 1) = Control Map at time 37
2 Control Map at time (37 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (37 + 1) = Control Map at time 37 and Control Map at time 37 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (37 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
3 37 + 1 = 38 37 + 1 = 38
4 Control Map at time (37 + 1) = Control Map at time 38 if 37 + 1 = 38, then Control Map at time (37 + 1) = Control Map at time 38
5 Control Map at time 38 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (37 + 1) = Control Map at time 38 and Control Map at time (37 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 38 = [ entry 0: (pair ("while", 2)), [ ] ]

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