Proof: Get Begin Expr Value 12

Let's prove the following theorem:

if the following are true:

expression state at time 12 = "begin_expr"
the expression at time 12 = Dog()
Value Stack at time 12 = [ ]

then Value Stack at time 13 = [ [ ], [ ] ]

Proof:

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Given

1	expression state at time 12 = "begin_expr"
2	the expression at time 12 = `Dog()`
3	Value Stack at time 12 = [ ]

Proof Table

#	Claim	Reason
1	Value Stack at time (12 + 1) = [ [ ], Value Stack at time 12 ]	if expression state at time 12 = "begin_expr" and the expression at time 12 = `Dog()`, then Value Stack at time (12 + 1) = [ [ ], Value Stack at time 12 ] (Begin Constructor Elements (1))
2	[ [ ], Value Stack at time 12 ] = [ [ ], [ ] ]	if Value Stack at time 12 = [ ], then [ [ ], Value Stack at time 12 ] = [ [ ], [ ] ] (Substitution)
3	Value Stack at time (12 + 1) = [ [ ], [ ] ]	if Value Stack at time (12 + 1) = [ [ ], Value Stack at time 12 ] and [ [ ], Value Stack at time 12 ] = [ [ ], [ ] ], then Value Stack at time (12 + 1) = [ [ ], [ ] ] (Transitive Property of Equality)
4	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
5	Value Stack at time (12 + 1) = Value Stack at time 13	if 12 + 1 = 13, then Value Stack at time (12 + 1) = Value Stack at time 13 (Substitution)
6	Value Stack at time 13 = [ [ ], [ ] ]	if Value Stack at time (12 + 1) = Value Stack at time 13 and Value Stack at time (12 + 1) = [ [ ], [ ] ], then Value Stack at time 13 = [ [ ], [ ] ] (Transitive Property of Equality Variation 2)

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