Proof: Write Stmt Control Map At Unchanged 45

Let's prove the following theorem:

if the following are true:
  • the line at time 45 = 3
  • the tab at time 45 = 1
  • statement at line 3, tab 1 = a = __add__(a, 1)
  • Control Map at time 45 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 46 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 the line at time 45 = 3
2 the tab at time 45 = 1
3 statement at line 3, tab 1 = a = __add__(a, 1)
4 Control Map at time 45 = [ entry 0: (pair ("while", 2)), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (45 + 1) = Control Map at time 45 if the line at time 45 = 3 and the tab at time 45 = 1 and statement at line 3, tab 1 = a = __add__(a, 1), then Control Map at time (45 + 1) = Control Map at time 45
2 Control Map at time (45 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (45 + 1) = Control Map at time 45 and Control Map at time 45 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (45 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
3 45 + 1 = 46 45 + 1 = 46
4 Control Map at time (45 + 1) = Control Map at time 46 if 45 + 1 = 46, then Control Map at time (45 + 1) = Control Map at time 46
5 Control Map at time 46 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (45 + 1) = Control Map at time 46 and Control Map at time (45 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 46 = [ entry 0: (pair ("while", 2)), [ ] ]

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