Proof: Get Begin Expr Params Unchanged55

Let's prove the following theorem:

if the following are true:
  • the expression at time 55 = 5
  • expression state at time 55 = "begin_expr"
  • 5 is constant
  • arguments stack at time 55 = [ [ ], [ [ ], [ ] ] ]

then arguments stack at time 56 = [ [ ], [ [ ], [ ] ] ]

Proof:

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Given
1 the expression at time 55 = 5
2 expression state at time 55 = "begin_expr"
3 5 is constant
4 arguments stack at time 55 = [ [ ], [ [ ], [ ] ] ]
Proof Table
# Claim Reason
1 arguments stack at time (55 + 1) = arguments stack at time 55 if expression state at time 55 = "begin_expr" and the expression at time 55 = 5 and 5 is constant, then arguments stack at time (55 + 1) = arguments stack at time 55
2 arguments stack at time (55 + 1) = [ [ ], [ [ ], [ ] ] ] if arguments stack at time (55 + 1) = arguments stack at time 55 and arguments stack at time 55 = [ [ ], [ [ ], [ ] ] ], then arguments stack at time (55 + 1) = [ [ ], [ [ ], [ ] ] ]
3 55 + 1 = 56 55 + 1 = 56
4 arguments stack at time (55 + 1) = arguments stack at time 56 if 55 + 1 = 56, then arguments stack at time (55 + 1) = arguments stack at time 56
5 arguments stack at time 56 = [ [ ], [ [ ], [ ] ] ] if arguments stack at time (55 + 1) = arguments stack at time 56 and arguments stack at time (55 + 1) = [ [ ], [ [ ], [ ] ] ], then arguments stack at time 56 = [ [ ], [ [ ], [ ] ] ]

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