Proof: Get Begin Expr Parent 37

Let's prove the following theorem:

if the following are true:
  • expression state at time 37 = "begin_expr"
  • the expression at time 37 = joe.move()
  • parent stack at time 37 = [ ]

then parent stack at time 38 = [ joe.move(), [ ] ]

Proof:

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Given
1 expression state at time 37 = "begin_expr"
2 the expression at time 37 = joe.move()
3 parent stack at time 37 = [ ]
Proof Table
# Claim Reason
1 parent stack at time (37 + 1) = [ joe.move(), parent stack at time 37 ] if expression state at time 37 = "begin_expr" and the expression at time 37 = joe.move(), then parent stack at time (37 + 1) = [ joe.move(), parent stack at time 37 ]
2 [ joe.move(), parent stack at time 37 ] = [ joe.move(), [ ] ] if parent stack at time 37 = [ ], then [ joe.move(), parent stack at time 37 ] = [ joe.move(), [ ] ]
3 parent stack at time (37 + 1) = [ joe.move(), [ ] ] if parent stack at time (37 + 1) = [ joe.move(), parent stack at time 37 ] and [ joe.move(), parent stack at time 37 ] = [ joe.move(), [ ] ], then parent stack at time (37 + 1) = [ joe.move(), [ ] ]
4 37 + 1 = 38 37 + 1 = 38
5 parent stack at time (37 + 1) = parent stack at time 38 if 37 + 1 = 38, then parent stack at time (37 + 1) = parent stack at time 38
6 parent stack at time 38 = [ joe.move(), [ ] ] if parent stack at time (37 + 1) = parent stack at time 38 and parent stack at time (37 + 1) = [ joe.move(), [ ] ], then parent stack at time 38 = [ joe.move(), [ ] ]

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