Proof: Get Begin Expr Parent 35

Let's prove the following theorem:

if the following are true:
  • expression state at time 35 = "begin_expr"
  • the expression at time 35 = self."last_name" = last_name
  • parent stack at time 35 = [ ]

then parent stack at time 36 = [ self."last_name" = last_name, [ ] ]

Proof:

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Given
1 expression state at time 35 = "begin_expr"
2 the expression at time 35 = self."last_name" = last_name
3 parent stack at time 35 = [ ]
Proof Table
# Claim Reason
1 parent stack at time (35 + 1) = [ self."last_name" = last_name, parent stack at time 35 ] if expression state at time 35 = "begin_expr" and the expression at time 35 = self."last_name" = last_name, then parent stack at time (35 + 1) = [ self."last_name" = last_name, parent stack at time 35 ]
2 [ self."last_name" = last_name, parent stack at time 35 ] = [ self."last_name" = last_name, [ ] ] if parent stack at time 35 = [ ], then [ self."last_name" = last_name, parent stack at time 35 ] = [ self."last_name" = last_name, [ ] ]
3 parent stack at time (35 + 1) = [ self."last_name" = last_name, [ ] ] if parent stack at time (35 + 1) = [ self."last_name" = last_name, parent stack at time 35 ] and [ self."last_name" = last_name, parent stack at time 35 ] = [ self."last_name" = last_name, [ ] ], then parent stack at time (35 + 1) = [ self."last_name" = last_name, [ ] ]
4 35 + 1 = 36 35 + 1 = 36
5 parent stack at time (35 + 1) = parent stack at time 36 if 35 + 1 = 36, then parent stack at time (35 + 1) = parent stack at time 36
6 parent stack at time 36 = [ self."last_name" = last_name, [ ] ] if parent stack at time (35 + 1) = parent stack at time 36 and parent stack at time (35 + 1) = [ self."last_name" = last_name, [ ] ], then parent stack at time 36 = [ self."last_name" = last_name, [ ] ]

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