Proof: Get Begin Expr State 11

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
parent stack at time 11 = [ Person("John", "Smith", 25), [ ] ]

then expression state at time 12 = "return"

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	parent stack at time 11 = [ `Person("John", "Smith", 25)`, [ ] ]

Proof Table

#	Claim	Reason
1	expression state at time (11 + 1) = "return"	if expression state at time 11 = "begin_expr" and the expression at time 11 = "John" and "John" is constant and parent stack at time 11 = [ `Person("John", "Smith", 25)`, [ ] ], then expression state at time (11 + 1) = "return" (Evaluate Constant Argument State Property)
2	11 + 1 = 12	11 + 1 = 12 (Fixed Value Statement)
3	expression state at time (11 + 1) = expression state at time 12	if 11 + 1 = 12, then expression state at time (11 + 1) = expression state at time 12 (Substitution)
4	expression state at time 12 = "return"	if expression state at time (11 + 1) = expression state at time 12 and expression state at time (11 + 1) = "return", then expression state at time 12 = "return" (Transitive Property of Equality Variation 2)

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