Proof: Write Decrement If Unchanged Variables At 14

Let's prove the following theorem:

if the following are true:
  • the line at time 14 = 5
  • the tab at time 14 = 1
  • Variables Map at time 14 = [ entry a: 9, [ ] ]
  • number of lines = 5 - 1
  • Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ]

then Variables Map at time 15 = [ entry a: 9, [ ] ]

Proof:

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Given
1 the line at time 14 = 5
2 the tab at time 14 = 1
3 Variables Map at time 14 = [ entry a: 9, [ ] ]
4 number of lines = 5 - 1
5 Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ]
Proof Table
# Claim Reason
1 value at (1 - 1) in map (Control Map at time 14) = pair ("if", False) if Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ], then value at (1 - 1) in map (Control Map at time 14) = pair ("if", False)
2 Variables Map at time (14 + 1) = Variables Map at time 14 if the line at time 14 = 5 and the tab at time 14 = 1 and number of lines = 5 - 1 and value at (1 - 1) in map (Control Map at time 14) = pair ("if", False), then Variables Map at time (14 + 1) = Variables Map at time 14
3 Variables Map at time (14 + 1) = [ entry a: 9, [ ] ] if Variables Map at time (14 + 1) = Variables Map at time 14 and Variables Map at time 14 = [ entry a: 9, [ ] ], then Variables Map at time (14 + 1) = [ entry a: 9, [ ] ]
4 14 + 1 = 15 14 + 1 = 15
5 Variables Map at time (14 + 1) = Variables Map at time 15 if 14 + 1 = 15, then Variables Map at time (14 + 1) = Variables Map at time 15
6 Variables Map at time 15 = [ entry a: 9, [ ] ] if Variables Map at time (14 + 1) = Variables Map at time 15 and Variables Map at time (14 + 1) = [ entry a: 9, [ ] ], then Variables Map at time 15 = [ entry a: 9, [ ] ]

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