Proof: Get Begin Expr Value 45

Let's prove the following theorem:

if the following are true:

expression state at time 45 = "begin_expr"
the expression at time 45 = __add__(self.x, 5)
Value Stack at time 45 = [ [ ], [ ] ]

then Value Stack at time 46 = [ [ ], [ [ ], [ ] ] ]

Proof:

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Given

1	expression state at time 45 = "begin_expr"
2	the expression at time 45 = `__add__(self.x, 5)`
3	Value Stack at time 45 = [ [ ], [ ] ]

Proof Table

#	Claim	Reason
1	Value Stack at time (45 + 1) = [ [ ], Value Stack at time 45 ]	if expression state at time 45 = "begin_expr" and the expression at time 45 = `__add__(self.x, 5)`, then Value Stack at time (45 + 1) = [ [ ], Value Stack at time 45 ] (Begin Expression Values Rule)
2	[ [ ], Value Stack at time 45 ] = [ [ ], [ [ ], [ ] ] ]	if Value Stack at time 45 = [ [ ], [ ] ], then [ [ ], Value Stack at time 45 ] = [ [ ], [ [ ], [ ] ] ] (Substitution)
3	Value Stack at time (45 + 1) = [ [ ], [ [ ], [ ] ] ]	if Value Stack at time (45 + 1) = [ [ ], Value Stack at time 45 ] and [ [ ], Value Stack at time 45 ] = [ [ ], [ [ ], [ ] ] ], then Value Stack at time (45 + 1) = [ [ ], [ [ ], [ ] ] ] (Transitive Property of Equality)
4	45 + 1 = 46	45 + 1 = 46 (Fixed Value Statement)
5	Value Stack at time (45 + 1) = Value Stack at time 46	if 45 + 1 = 46, then Value Stack at time (45 + 1) = Value Stack at time 46 (Substitution)
6	Value Stack at time 46 = [ [ ], [ [ ], [ ] ] ]	if Value Stack at time (45 + 1) = Value Stack at time 46 and Value Stack at time (45 + 1) = [ [ ], [ [ ], [ ] ] ], then Value Stack at time 46 = [ [ ], [ [ ], [ ] ] ] (Transitive Property of Equality Variation 2)

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