Proof: Write End While Control Map 23

Let's prove the following theorem:

if the following are true:
  • the line at time 23 = 4
  • the tab at time 23 = 1
  • number of lines = 3
  • Control Map at time 23 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 24 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 the line at time 23 = 4
2 the tab at time 23 = 1
3 number of lines = 3
4 Control Map at time 23 = [ entry 0: (pair ("while", 2)), [ ] ]
Proof Table
# Claim Reason
1 4 - 1 = 3 4 - 1 = 3
2 number of lines = 4 - 1 if number of lines = 3 and 4 - 1 = 3, then number of lines = 4 - 1
3 value at (1 - 1) in map (Control Map at time 23) = pair ("while", 2) if Control Map at time 23 = [ entry 0: (pair ("while", 2)), [ ] ], then value at (1 - 1) in map (Control Map at time 23) = pair ("while", 2)
4 Control Map at time (23 + 1) = Control Map at time 23 if the line at time 23 = 4 and the tab at time 23 = 1 and number of lines = 4 - 1 and value at (1 - 1) in map (Control Map at time 23) = pair ("while", 2), then Control Map at time (23 + 1) = Control Map at time 23
5 Control Map at time (23 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (23 + 1) = Control Map at time 23 and Control Map at time 23 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (23 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
6 23 + 1 = 24 23 + 1 = 24
7 Control Map at time (23 + 1) = Control Map at time 24 if 23 + 1 = 24, then Control Map at time (23 + 1) = Control Map at time 24
8 Control Map at time 24 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (23 + 1) = Control Map at time 24 and Control Map at time (23 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 24 = [ entry 0: (pair ("while", 2)), [ ] ]

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