Proof: Get Begin Expr State 3

Let's prove the following theorem:

if the following are true:

the expression at time 3 = 1
expression state at time 3 = "begin_expr"
1 is constant
parent stack at time 3 = [ __eq__(1, 3), [ ] ]

then expression state at time 4 = "return"

Proof:

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Given

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

Proof Table

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

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