Proof: Get Begin Expr Params Unchanged14

Let's prove the following theorem:

if the following are true:
  • the expression at time 14 = "Smith"
  • expression state at time 14 = "begin_expr"
  • "Smith" is constant
  • arguments stack at time 14 = [ [ 25, [ ] ], [ ] ]

then arguments stack at time 15 = [ [ 25, [ ] ], [ ] ]

Proof:

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Given
1 the expression at time 14 = "Smith"
2 expression state at time 14 = "begin_expr"
3 "Smith" is constant
4 arguments stack at time 14 = [ [ 25, [ ] ], [ ] ]
Proof Table
# Claim Reason
1 arguments stack at time (14 + 1) = arguments stack at time 14 if expression state at time 14 = "begin_expr" and the expression at time 14 = "Smith" and "Smith" is constant, then arguments stack at time (14 + 1) = arguments stack at time 14
2 arguments stack at time (14 + 1) = [ [ 25, [ ] ], [ ] ] if arguments stack at time (14 + 1) = arguments stack at time 14 and arguments stack at time 14 = [ [ 25, [ ] ], [ ] ], then arguments stack at time (14 + 1) = [ [ 25, [ ] ], [ ] ]
3 14 + 1 = 15 14 + 1 = 15
4 arguments stack at time (14 + 1) = arguments stack at time 15 if 14 + 1 = 15, then arguments stack at time (14 + 1) = arguments stack at time 15
5 arguments stack at time 15 = [ [ 25, [ ] ], [ ] ] if arguments stack at time (14 + 1) = arguments stack at time 15 and arguments stack at time (14 + 1) = [ [ 25, [ ] ], [ ] ], then arguments stack at time 15 = [ [ 25, [ ] ], [ ] ]

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