Proof: Get Begin Expr Value 13

Let's prove the following theorem:

if the following are true:

expression state at time 13 = "begin_expr"
the expression at time 13 = __eq__(7, 9)
Value Stack at time 13 = [ ]

then Value Stack at time 14 = [ [ ], [ ] ]

Proof:

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Given

1	expression state at time 13 = "begin_expr"
2	the expression at time 13 = `__eq__(7, 9)`
3	Value Stack at time 13 = [ ]

Proof Table

#	Claim	Reason
1	Value Stack at time (13 + 1) = [ [ ], Value Stack at time 13 ]	if expression state at time 13 = "begin_expr" and the expression at time 13 = `__eq__(7, 9)`, then Value Stack at time (13 + 1) = [ [ ], Value Stack at time 13 ] (Begin Expression Values Rule)
2	[ [ ], Value Stack at time 13 ] = [ [ ], [ ] ]	if Value Stack at time 13 = [ ], then [ [ ], Value Stack at time 13 ] = [ [ ], [ ] ] (Substitution)
3	Value Stack at time (13 + 1) = [ [ ], [ ] ]	if Value Stack at time (13 + 1) = [ [ ], Value Stack at time 13 ] and [ [ ], Value Stack at time 13 ] = [ [ ], [ ] ], then Value Stack at time (13 + 1) = [ [ ], [ ] ] (Transitive Property of Equality)
4	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
5	Value Stack at time (13 + 1) = Value Stack at time 14	if 13 + 1 = 14, then Value Stack at time (13 + 1) = Value Stack at time 14 (Substitution)
6	Value Stack at time 14 = [ [ ], [ ] ]	if Value Stack at time (13 + 1) = Value Stack at time 14 and Value Stack at time (13 + 1) = [ [ ], [ ] ], then Value Stack at time 14 = [ [ ], [ ] ] (Transitive Property of Equality Variation 2)

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