Proof: Get Begin Expr State 18

Let's prove the following theorem:

if the following are true:

the expression at time 18 = 9
expression state at time 18 = "begin_expr"
9 is constant
parent stack at time 18 = [ __eq__(7, 9), [ ] ]

then expression state at time 19 = "return"

Proof:

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Given

1	the expression at time 18 = 9
2	expression state at time 18 = "begin_expr"
3	9 is constant
4	parent stack at time 18 = [ `__eq__(7, 9)`, [ ] ]

Proof Table

#	Claim	Reason
1	expression state at time (18 + 1) = "return"	if expression state at time 18 = "begin_expr" and the expression at time 18 = 9 and 9 is constant and parent stack at time 18 = [ `__eq__(7, 9)`, [ ] ], then expression state at time (18 + 1) = "return" (Evaluate Constant Argument State Property)
2	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
3	expression state at time (18 + 1) = expression state at time 19	if 18 + 1 = 19, then expression state at time (18 + 1) = expression state at time 19 (Substitution)
4	expression state at time 19 = "return"	if expression state at time (18 + 1) = expression state at time 19 and expression state at time (18 + 1) = "return", then expression state at time 19 = "return" (Transitive Property of Equality Variation 2)

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