Proof: Get Begin Expr Parent 26

Let's prove the following theorem:

if the following are true:
  • expression state at time 26 = "begin_expr"
  • the expression at time 26 = self."y" = 0
  • parent stack at time 26 = [ ]

then parent stack at time 27 = [ self."y" = 0, [ ] ]

Proof:

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Given
1 expression state at time 26 = "begin_expr"
2 the expression at time 26 = self."y" = 0
3 parent stack at time 26 = [ ]
Proof Table
# Claim Reason
1 parent stack at time (26 + 1) = [ self."y" = 0, parent stack at time 26 ] if expression state at time 26 = "begin_expr" and the expression at time 26 = self."y" = 0, then parent stack at time (26 + 1) = [ self."y" = 0, parent stack at time 26 ]
2 [ self."y" = 0, parent stack at time 26 ] = [ self."y" = 0, [ ] ] if parent stack at time 26 = [ ], then [ self."y" = 0, parent stack at time 26 ] = [ self."y" = 0, [ ] ]
3 parent stack at time (26 + 1) = [ self."y" = 0, [ ] ] if parent stack at time (26 + 1) = [ self."y" = 0, parent stack at time 26 ] and [ self."y" = 0, parent stack at time 26 ] = [ self."y" = 0, [ ] ], then parent stack at time (26 + 1) = [ self."y" = 0, [ ] ]
4 26 + 1 = 27 26 + 1 = 27
5 parent stack at time (26 + 1) = parent stack at time 27 if 26 + 1 = 27, then parent stack at time (26 + 1) = parent stack at time 27
6 parent stack at time 27 = [ self."y" = 0, [ ] ] if parent stack at time (26 + 1) = parent stack at time 27 and parent stack at time (26 + 1) = [ self."y" = 0, [ ] ], then parent stack at time 27 = [ self."y" = 0, [ ] ]

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