Proof: Write End While Control Map 46

Let's prove the following theorem:

if the following are true:
  • the line at time 46 = 4
  • the tab at time 46 = 1
  • number of lines = 3
  • Control Map at time 46 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 47 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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Given
1 the line at time 46 = 4
2 the tab at time 46 = 1
3 number of lines = 3
4 Control Map at time 46 = [ 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 46) = pair ("while", 2) if Control Map at time 46 = [ entry 0: (pair ("while", 2)), [ ] ], then value at (1 - 1) in map (Control Map at time 46) = pair ("while", 2)
4 Control Map at time (46 + 1) = Control Map at time 46 if the line at time 46 = 4 and the tab at time 46 = 1 and number of lines = 4 - 1 and value at (1 - 1) in map (Control Map at time 46) = pair ("while", 2), then Control Map at time (46 + 1) = Control Map at time 46
5 Control Map at time (46 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (46 + 1) = Control Map at time 46 and Control Map at time 46 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (46 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]
6 46 + 1 = 47 46 + 1 = 47
7 Control Map at time (46 + 1) = Control Map at time 47 if 46 + 1 = 47, then Control Map at time (46 + 1) = Control Map at time 47
8 Control Map at time 47 = [ entry 0: (pair ("while", 2)), [ ] ] if Control Map at time (46 + 1) = Control Map at time 47 and Control Map at time (46 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 47 = [ entry 0: (pair ("while", 2)), [ ] ]

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