Proof: Get Begin Expr Parent 1

Let's prove the following theorem:

if the following are true:
  • expression state at time 1 = "begin_expr"
  • the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"}
  • parent stack at time 1 = [ ]

then parent stack at time 2 = [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ]

Proof:

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

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