Proof: Get Iterate Parent 18

Let's prove the following theorem:

if the following are true:
  • expression state at time 18 = "iterate_args"
  • arguments stack at time 18 = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ]
  • parent stack at time 18 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

then parent stack at time 19 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

Proof:

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Given
1 expression state at time 18 = "iterate_args"
2 arguments stack at time 18 = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ]
3 parent stack at time 18 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]
Proof Table
# Claim Reason
1 parent stack at time (18 + 1) = parent stack at time 18 if expression state at time 18 = "iterate_args" and arguments stack at time 18 = [ [ "Mexico", [ ] ], [ [ ], [ ] ] ], then parent stack at time (18 + 1) = parent stack at time 18
2 parent stack at time (18 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time (18 + 1) = parent stack at time 18 and parent stack at time 18 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ], then parent stack at time (18 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]
3 18 + 1 = 19 18 + 1 = 19
4 parent stack at time (18 + 1) = parent stack at time 19 if 18 + 1 = 19, then parent stack at time (18 + 1) = parent stack at time 19
5 parent stack at time 19 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time (18 + 1) = parent stack at time 19 and parent stack at time (18 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ], then parent stack at time 19 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

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