Proof: Get Begin Expr Value 47

Let's prove the following theorem:

if the following are true:

expression state at time 47 = "begin_expr"
the expression at time 47 = self.x
Value Stack at time 47 = [ [ ], [ [ ], [ ] ] ]

then Value Stack at time 48 = [ [ ], [ [ ], [ [ ], [ ] ] ] ]

Proof:

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Given

1	expression state at time 47 = "begin_expr"
2	the expression at time 47 = `self.x`
3	Value Stack at time 47 = [ [ ], [ [ ], [ ] ] ]

Proof Table

#	Claim	Reason
1	Value Stack at time (47 + 1) = [ [ ], Value Stack at time 47 ]	if expression state at time 47 = "begin_expr" and the expression at time 47 = `self.x`, then Value Stack at time (47 + 1) = [ [ ], Value Stack at time 47 ] (Begin Get Attribute (1))
2	[ [ ], Value Stack at time 47 ] = [ [ ], [ [ ], [ [ ], [ ] ] ] ]	if Value Stack at time 47 = [ [ ], [ [ ], [ ] ] ], then [ [ ], Value Stack at time 47 ] = [ [ ], [ [ ], [ [ ], [ ] ] ] ] (Substitution)
3	Value Stack at time (47 + 1) = [ [ ], [ [ ], [ [ ], [ ] ] ] ]	if Value Stack at time (47 + 1) = [ [ ], Value Stack at time 47 ] and [ [ ], Value Stack at time 47 ] = [ [ ], [ [ ], [ [ ], [ ] ] ] ], then Value Stack at time (47 + 1) = [ [ ], [ [ ], [ [ ], [ ] ] ] ] (Transitive Property of Equality)
4	47 + 1 = 48	47 + 1 = 48 (Fixed Value Statement)
5	Value Stack at time (47 + 1) = Value Stack at time 48	if 47 + 1 = 48, then Value Stack at time (47 + 1) = Value Stack at time 48 (Substitution)
6	Value Stack at time 48 = [ [ ], [ [ ], [ [ ], [ ] ] ] ]	if Value Stack at time (47 + 1) = Value Stack at time 48 and Value Stack at time (47 + 1) = [ [ ], [ [ ], [ [ ], [ ] ] ] ], then Value Stack at time 48 = [ [ ], [ [ ], [ [ ], [ ] ] ] ] (Transitive Property of Equality Variation 2)

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