Proof: Write Stmt Control Map At Unchanged 13

Let's prove the following theorem:

if the following are true:
  • the line at time 13 = 2
  • the tab at time 13 = 1
  • statement at line 2, tab 1 = z = __add__(x, 3)
  • Control Map at time 13 = [ entry 0: (pair ("function", "add_three")), [ ] ]

then Control Map at time 14 = [ entry 0: (pair ("function", "add_three")), [ ] ]

Proof:

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Given
1 the line at time 13 = 2
2 the tab at time 13 = 1
3 statement at line 2, tab 1 = z = __add__(x, 3)
4 Control Map at time 13 = [ entry 0: (pair ("function", "add_three")), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (13 + 1) = Control Map at time 13 if the line at time 13 = 2 and the tab at time 13 = 1 and statement at line 2, tab 1 = z = __add__(x, 3), then Control Map at time (13 + 1) = Control Map at time 13
2 Control Map at time (13 + 1) = [ entry 0: (pair ("function", "add_three")), [ ] ] if Control Map at time (13 + 1) = Control Map at time 13 and Control Map at time 13 = [ entry 0: (pair ("function", "add_three")), [ ] ], then Control Map at time (13 + 1) = [ entry 0: (pair ("function", "add_three")), [ ] ]
3 13 + 1 = 14 13 + 1 = 14
4 Control Map at time (13 + 1) = Control Map at time 14 if 13 + 1 = 14, then Control Map at time (13 + 1) = Control Map at time 14
5 Control Map at time 14 = [ entry 0: (pair ("function", "add_three")), [ ] ] if Control Map at time (13 + 1) = Control Map at time 14 and Control Map at time (13 + 1) = [ entry 0: (pair ("function", "add_three")), [ ] ], then Control Map at time 14 = [ entry 0: (pair ("function", "add_three")), [ ] ]

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