Proof: Get Begin Expr Parent 28

Let's prove the following theorem:

if the following are true:
  • expression state at time 28 = "begin_expr"
  • the expression at time 28 = __setitem__(locations, "ES", "Spain")
  • parent stack at time 28 = [ ]

then parent stack at time 29 = [ __setitem__(locations, "ES", "Spain"), [ ] ]

Proof:

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Given
1 expression state at time 28 = "begin_expr"
2 the expression at time 28 = __setitem__(locations, "ES", "Spain")
3 parent stack at time 28 = [ ]
Proof Table
# Claim Reason
1 parent stack at time (28 + 1) = [ __setitem__(locations, "ES", "Spain"), parent stack at time 28 ] if expression state at time 28 = "begin_expr" and the expression at time 28 = __setitem__(locations, "ES", "Spain"), then parent stack at time (28 + 1) = [ __setitem__(locations, "ES", "Spain"), parent stack at time 28 ]
2 [ __setitem__(locations, "ES", "Spain"), parent stack at time 28 ] = [ __setitem__(locations, "ES", "Spain"), [ ] ] if parent stack at time 28 = [ ], then [ __setitem__(locations, "ES", "Spain"), parent stack at time 28 ] = [ __setitem__(locations, "ES", "Spain"), [ ] ]
3 parent stack at time (28 + 1) = [ __setitem__(locations, "ES", "Spain"), [ ] ] if parent stack at time (28 + 1) = [ __setitem__(locations, "ES", "Spain"), parent stack at time 28 ] and [ __setitem__(locations, "ES", "Spain"), parent stack at time 28 ] = [ __setitem__(locations, "ES", "Spain"), [ ] ], then parent stack at time (28 + 1) = [ __setitem__(locations, "ES", "Spain"), [ ] ]
4 28 + 1 = 29 28 + 1 = 29
5 parent stack at time (28 + 1) = parent stack at time 29 if 28 + 1 = 29, then parent stack at time (28 + 1) = parent stack at time 29
6 parent stack at time 29 = [ __setitem__(locations, "ES", "Spain"), [ ] ] if parent stack at time (28 + 1) = parent stack at time 29 and parent stack at time (28 + 1) = [ __setitem__(locations, "ES", "Spain"), [ ] ], then parent stack at time 29 = [ __setitem__(locations, "ES", "Spain"), [ ] ]

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