Proof: Get Iterate Parent 15

Let's prove the following theorem:

if the following are true:
  • expression state at time 15 = "iterate_args"
  • arguments stack at time 15 = [ [ "MX", [ "Mexico", [ ] ] ], [ [ ], [ ] ] ]
  • parent stack at time 15 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

then parent stack at time 16 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

Proof:

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Given
1 expression state at time 15 = "iterate_args"
2 arguments stack at time 15 = [ [ "MX", [ "Mexico", [ ] ] ], [ [ ], [ ] ] ]
3 parent stack at time 15 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]
Proof Table
# Claim Reason
1 parent stack at time (15 + 1) = parent stack at time 15 if expression state at time 15 = "iterate_args" and arguments stack at time 15 = [ [ "MX", [ "Mexico", [ ] ] ], [ [ ], [ ] ] ], then parent stack at time (15 + 1) = parent stack at time 15
2 parent stack at time (15 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time (15 + 1) = parent stack at time 15 and parent stack at time 15 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ], then parent stack at time (15 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]
3 15 + 1 = 16 15 + 1 = 16
4 parent stack at time (15 + 1) = parent stack at time 16 if 15 + 1 = 16, then parent stack at time (15 + 1) = parent stack at time 16
5 parent stack at time 16 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time (15 + 1) = parent stack at time 16 and parent stack at time (15 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ], then parent stack at time 16 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

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