Proof: Get Begin Expr Params Unchanged20

Let's prove the following theorem:

if the following are true:
  • the expression at time 20 = 0
  • expression state at time 20 = "begin_expr"
  • 0 is constant
  • arguments stack at time 20 = [ [ ], [ ] ]

then arguments stack at time 21 = [ [ ], [ ] ]

Proof:

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Given
1 the expression at time 20 = 0
2 expression state at time 20 = "begin_expr"
3 0 is constant
4 arguments stack at time 20 = [ [ ], [ ] ]
Proof Table
# Claim Reason
1 arguments stack at time (20 + 1) = arguments stack at time 20 if expression state at time 20 = "begin_expr" and the expression at time 20 = 0 and 0 is constant, then arguments stack at time (20 + 1) = arguments stack at time 20
2 arguments stack at time (20 + 1) = [ [ ], [ ] ] if arguments stack at time (20 + 1) = arguments stack at time 20 and arguments stack at time 20 = [ [ ], [ ] ], then arguments stack at time (20 + 1) = [ [ ], [ ] ]
3 20 + 1 = 21 20 + 1 = 21
4 arguments stack at time (20 + 1) = arguments stack at time 21 if 20 + 1 = 21, then arguments stack at time (20 + 1) = arguments stack at time 21
5 arguments stack at time 21 = [ [ ], [ ] ] if arguments stack at time (20 + 1) = arguments stack at time 21 and arguments stack at time (20 + 1) = [ [ ], [ ] ], then arguments stack at time 21 = [ [ ], [ ] ]

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