Proof: Get Begin Expr Value 37

Let's prove the following theorem:

if the following are true:

expression state at time 37 = "begin_expr"
the expression at time 37 = joe.move()
Value Stack at time 37 = [ ]

then Value Stack at time 38 = [ [ ], [ ] ]

Proof:

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Given

1	expression state at time 37 = "begin_expr"
2	the expression at time 37 = `joe.move()`
3	Value Stack at time 37 = [ ]

Proof Table

#	Claim	Reason
1	Value Stack at time (37 + 1) = [ [ ], Value Stack at time 37 ]	if expression state at time 37 = "begin_expr" and the expression at time 37 = `joe.move()`, then Value Stack at time (37 + 1) = [ [ ], Value Stack at time 37 ] (Begin Method Arguments (1))
2	[ [ ], Value Stack at time 37 ] = [ [ ], [ ] ]	if Value Stack at time 37 = [ ], then [ [ ], Value Stack at time 37 ] = [ [ ], [ ] ] (Substitution)
3	Value Stack at time (37 + 1) = [ [ ], [ ] ]	if Value Stack at time (37 + 1) = [ [ ], Value Stack at time 37 ] and [ [ ], Value Stack at time 37 ] = [ [ ], [ ] ], then Value Stack at time (37 + 1) = [ [ ], [ ] ] (Transitive Property of Equality)
4	37 + 1 = 38	37 + 1 = 38 (Fixed Value Statement)
5	Value Stack at time (37 + 1) = Value Stack at time 38	if 37 + 1 = 38, then Value Stack at time (37 + 1) = Value Stack at time 38 (Substitution)
6	Value Stack at time 38 = [ [ ], [ ] ]	if Value Stack at time (37 + 1) = Value Stack at time 38 and Value Stack at time (37 + 1) = [ [ ], [ ] ], then Value Stack at time 38 = [ [ ], [ ] ] (Transitive Property of Equality Variation 2)

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