Proof: Get Begin Expr State 55

Let's prove the following theorem:

if the following are true:

the expression at time 55 = 5
expression state at time 55 = "begin_expr"
5 is constant
parent stack at time 55 = [ __add__(self.x, 5), [ self."x" = __add__(self.x, 5), [ ] ] ]

then expression state at time 56 = "return"

Proof:

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Given

1	the expression at time 55 = 5
2	expression state at time 55 = "begin_expr"
3	5 is constant
4	parent stack at time 55 = [ `__add__(self.x, 5)`, [ self."x" = `__add__(self.x, 5)`, [ ] ] ]

Proof Table

#	Claim	Reason
1	expression state at time (55 + 1) = "return"	if expression state at time 55 = "begin_expr" and the expression at time 55 = 5 and 5 is constant and parent stack at time 55 = [ `__add__(self.x, 5)`, [ self."x" = `__add__(self.x, 5)`, [ ] ] ], then expression state at time (55 + 1) = "return" (Evaluate Constant Argument State Property)
2	55 + 1 = 56	55 + 1 = 56 (Fixed Value Statement)
3	expression state at time (55 + 1) = expression state at time 56	if 55 + 1 = 56, then expression state at time (55 + 1) = expression state at time 56 (Substitution)
4	expression state at time 56 = "return"	if expression state at time (55 + 1) = expression state at time 56 and expression state at time (55 + 1) = "return", then expression state at time 56 = "return" (Transitive Property of Equality Variation 2)

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