Proof: Do Control Map At Unchanged 9

Let's prove the following theorem:

if the following are true:
  • expression state at time 9 = "iterate_args"
  • Control Map at time 9 = [ ]

then Control Map at time 10 = [ ]

Proof:

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Given
1 expression state at time 9 = "iterate_args"
2 Control Map at time 9 = [ ]
Proof Table
# Claim Reason
1 Control Map at time (9 + 1) = Control Map at time 9 if expression state at time 9 = "iterate_args", then Control Map at time (9 + 1) = Control Map at time 9
2 Control Map at time (9 + 1) = [ ] if Control Map at time (9 + 1) = Control Map at time 9 and Control Map at time 9 = [ ], then Control Map at time (9 + 1) = [ ]
3 9 + 1 = 10 9 + 1 = 10
4 Control Map at time (9 + 1) = Control Map at time 10 if 9 + 1 = 10, then Control Map at time (9 + 1) = Control Map at time 10
5 Control Map at time 10 = [ ] if Control Map at time (9 + 1) = Control Map at time 10 and Control Map at time (9 + 1) = [ ], then Control Map at time 10 = [ ]

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