Proof: Write Decrement Tab Variables At 12

Let's prove the following theorem:

if the following are true:
  • the line at time 12 = 3
  • the tab at time 12 = 1
  • statement at line 3, tab 0 = else:
  • Variables Map at time 12 = [ entry a: 7, [ ] ]
  • Control Map at time 12 = [ entry 0: (pair ("if", True)), [ ] ]

then Variables Map at time 13 = [ entry a: 7, [ ] ]

Proof:

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Given
1 the line at time 12 = 3
2 the tab at time 12 = 1
3 statement at line 3, tab 0 = else:
4 Variables Map at time 12 = [ entry a: 7, [ ] ]
5 Control Map at time 12 = [ entry 0: (pair ("if", True)), [ ] ]
Proof Table
# Claim Reason
1 0 < 1 0 < 1
2 value at (1 - 1) in map (Control Map at time 12) = pair ("if", True) if Control Map at time 12 = [ entry 0: (pair ("if", True)), [ ] ], then value at (1 - 1) in map (Control Map at time 12) = pair ("if", True)
3 Variables Map at time (12 + 1) = Variables Map at time 12 if the line at time 12 = 3 and the tab at time 12 = 1 and statement at line 3, tab 0 = else: and 0 < 1 and value at (1 - 1) in map (Control Map at time 12) = pair ("if", True), then Variables Map at time (12 + 1) = Variables Map at time 12
4 Variables Map at time (12 + 1) = [ entry a: 7, [ ] ] if Variables Map at time (12 + 1) = Variables Map at time 12 and Variables Map at time 12 = [ entry a: 7, [ ] ], then Variables Map at time (12 + 1) = [ entry a: 7, [ ] ]
5 12 + 1 = 13 12 + 1 = 13
6 Variables Map at time (12 + 1) = Variables Map at time 13 if 12 + 1 = 13, then Variables Map at time (12 + 1) = Variables Map at time 13
7 Variables Map at time 13 = [ entry a: 7, [ ] ] if Variables Map at time (12 + 1) = Variables Map at time 13 and Variables Map at time (12 + 1) = [ entry a: 7, [ ] ], then Variables Map at time 13 = [ entry a: 7, [ ] ]

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