Proof: Write Stmt Control Map At Unchanged Expr24

Let's prove the following theorem:

if the following are true:
  • the line at time 24 = 2
  • the tab at time 24 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 24 = "not_expr"
  • Control Map at time 24 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 25 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 the line at time 24 = 2
2 the tab at time 24 = 0
3 statement at line 2, tab 0 = while __lt__(a, 2):
4 expression state at time 24 = "not_expr"
5 Control Map at time 24 = [ entry 0: (pair ("while", 2)), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (24 + 1) = Control Map at time 24 if the line at time 24 = 2 and the tab at time 24 = 0 and statement at line 2, tab 0 = while __lt__(a, 2): and expression state at time 24 = "not_expr", then Control Map at time (24 + 1) = Control Map at time 24
2 Control Map at time (24 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (24 + 1) = Control Map at time 24 and Control Map at time 24 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (24 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
3 24 + 1 = 25 24 + 1 = 25
4 Control Map at time (24 + 1) = Control Map at time 25 if 24 + 1 = 25, then Control Map at time (24 + 1) = Control Map at time 25
5 Control Map at time 25 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (24 + 1) = Control Map at time 25 and Control Map at time (24 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 25 = [ entry 0: (pair ("while", 2)), [ ] ]

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