Proof: Do Control Map At Unchanged 21

Let's prove the following theorem:

if the following are true:
  • expression state at time 21 = "iterate_args"
  • Control Map at time 21 = [ entry 0: (pair ("function", "add_three")), [ ] ]

then Control Map at time 22 = [ entry 0: (pair ("function", "add_three")), [ ] ]

Proof:

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Given
1 expression state at time 21 = "iterate_args"
2 Control Map at time 21 = [ entry 0: (pair ("function", "add_three")), [ ] ]
Proof Table
# Claim Reason
1 Control Map at time (21 + 1) = Control Map at time 21 if expression state at time 21 = "iterate_args", then Control Map at time (21 + 1) = Control Map at time 21
2 Control Map at time (21 + 1) = [ entry 0: (pair ("function", "add_three")), [ ] ] if Control Map at time (21 + 1) = Control Map at time 21 and Control Map at time 21 = [ entry 0: (pair ("function", "add_three")), [ ] ], then Control Map at time (21 + 1) = [ entry 0: (pair ("function", "add_three")), [ ] ]
3 21 + 1 = 22 21 + 1 = 22
4 Control Map at time (21 + 1) = Control Map at time 22 if 21 + 1 = 22, then Control Map at time (21 + 1) = Control Map at time 22
5 Control Map at time 22 = [ entry 0: (pair ("function", "add_three")), [ ] ] if Control Map at time (21 + 1) = Control Map at time 22 and Control Map at time (21 + 1) = [ entry 0: (pair ("function", "add_three")), [ ] ], then Control Map at time 22 = [ entry 0: (pair ("function", "add_three")), [ ] ]

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