Proof: Do Stack At Unchanged 37

Let's prove the following theorem:

if the following are true:
  • expression state at time 37 = "begin_expr"
  • stack at time 37 = [ ]

then stack at time 38 = [ ]

Proof:

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

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