Proof: Get Begin Expr Params Unchanged11

Let's prove the following theorem:

if the following are true:
  • the expression at time 11 = "John"
  • expression state at time 11 = "begin_expr"
  • "John" is constant
  • arguments stack at time 11 = [ [ "Smith", [ 25, [ ] ] ], [ ] ]

then arguments stack at time 12 = [ [ "Smith", [ 25, [ ] ] ], [ ] ]

Proof:

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Given
1 the expression at time 11 = "John"
2 expression state at time 11 = "begin_expr"
3 "John" is constant
4 arguments stack at time 11 = [ [ "Smith", [ 25, [ ] ] ], [ ] ]
Proof Table
# Claim Reason
1 arguments stack at time (11 + 1) = arguments stack at time 11 if expression state at time 11 = "begin_expr" and the expression at time 11 = "John" and "John" is constant, then arguments stack at time (11 + 1) = arguments stack at time 11
2 arguments stack at time (11 + 1) = [ [ "Smith", [ 25, [ ] ] ], [ ] ] if arguments stack at time (11 + 1) = arguments stack at time 11 and arguments stack at time 11 = [ [ "Smith", [ 25, [ ] ] ], [ ] ], then arguments stack at time (11 + 1) = [ [ "Smith", [ 25, [ ] ] ], [ ] ]
3 11 + 1 = 12 11 + 1 = 12
4 arguments stack at time (11 + 1) = arguments stack at time 12 if 11 + 1 = 12, then arguments stack at time (11 + 1) = arguments stack at time 12
5 arguments stack at time 12 = [ [ "Smith", [ 25, [ ] ] ], [ ] ] if arguments stack at time (11 + 1) = arguments stack at time 12 and arguments stack at time (11 + 1) = [ [ "Smith", [ 25, [ ] ] ], [ ] ], then arguments stack at time 12 = [ [ "Smith", [ 25, [ ] ] ], [ ] ]

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