Proof: Write Stmt Control Map At Unchanged Expr47

Let's prove the following theorem:

if the following are true:
  • the line at time 47 = 2
  • the tab at time 47 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 47 = "not_expr"
  • Control Map at time 47 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 48 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 the line at time 47 = 2
2 the tab at time 47 = 0
3 statement at line 2, tab 0 = while __lt__(a, 2):
4 expression state at time 47 = "not_expr"
5 Control Map at time 47 = [ entry 0: (pair ("while", 2)), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (47 + 1) = Control Map at time 47 if the line at time 47 = 2 and the tab at time 47 = 0 and statement at line 2, tab 0 = while __lt__(a, 2): and expression state at time 47 = "not_expr", then Control Map at time (47 + 1) = Control Map at time 47
2 Control Map at time (47 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (47 + 1) = Control Map at time 47 and Control Map at time 47 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (47 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
3 47 + 1 = 48 47 + 1 = 48
4 Control Map at time (47 + 1) = Control Map at time 48 if 47 + 1 = 48, then Control Map at time (47 + 1) = Control Map at time 48
5 Control Map at time 48 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (47 + 1) = Control Map at time 48 and Control Map at time (47 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 48 = [ entry 0: (pair ("while", 2)), [ ] ]

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