Proof: Get Begin Expr Parent 14

Let's prove the following theorem:

if the following are true:
  • expression state at time 14 = "begin_expr"
  • the expression at time 14 = entry "MX": "Mexico"
  • parent stack at time 14 = [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ]

then parent stack at time 15 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

Proof:

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Given
1 expression state at time 14 = "begin_expr"
2 the expression at time 14 = entry "MX": "Mexico"
3 parent stack at time 14 = [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ]
Proof Table
# Claim Reason
1 parent stack at time (14 + 1) = [ entry "MX": "Mexico", parent stack at time 14 ] if expression state at time 14 = "begin_expr" and the expression at time 14 = entry "MX": "Mexico", then parent stack at time (14 + 1) = [ entry "MX": "Mexico", parent stack at time 14 ]
2 [ entry "MX": "Mexico", parent stack at time 14 ] = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time 14 = [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ], then [ entry "MX": "Mexico", parent stack at time 14 ] = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]
3 parent stack at time (14 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time (14 + 1) = [ entry "MX": "Mexico", parent stack at time 14 ] and [ entry "MX": "Mexico", parent stack at time 14 ] = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ], then parent stack at time (14 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]
4 14 + 1 = 15 14 + 1 = 15
5 parent stack at time (14 + 1) = parent stack at time 15 if 14 + 1 = 15, then parent stack at time (14 + 1) = parent stack at time 15
6 parent stack at time 15 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ] if parent stack at time (14 + 1) = parent stack at time 15 and parent stack at time (14 + 1) = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ], then parent stack at time 15 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

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