Proof: Get Begin Expr Value 1

Let's prove the following theorem:

if the following are true:

expression state at time 1 = "begin_expr"
the expression at time 1 = {"ES": "Estonia", "MX": "Mexico"}
Value Stack at time 1 = [ ]

then Value Stack at time 2 = [ [ ], [ ] ]

Proof:

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Given

1	expression state at time 1 = "begin_expr"
2	the expression at time 1 = `{"ES": "Estonia", "MX": "Mexico"}`
3	Value Stack at time 1 = [ ]

Proof Table

#	Claim	Reason
1	Value Stack at time (1 + 1) = [ [ ], Value Stack at time 1 ]	if expression state at time 1 = "begin_expr" and the expression at time 1 = `{"ES": "Estonia", "MX": "Mexico"}`, then Value Stack at time (1 + 1) = [ [ ], Value Stack at time 1 ] (Begin Dict Elements (1))
2	[ [ ], Value Stack at time 1 ] = [ [ ], [ ] ]	if Value Stack at time 1 = [ ], then [ [ ], Value Stack at time 1 ] = [ [ ], [ ] ] (Substitution)
3	Value Stack at time (1 + 1) = [ [ ], [ ] ]	if Value Stack at time (1 + 1) = [ [ ], Value Stack at time 1 ] and [ [ ], Value Stack at time 1 ] = [ [ ], [ ] ], then Value Stack at time (1 + 1) = [ [ ], [ ] ] (Transitive Property of Equality)
4	1 + 1 = 2	1 + 1 = 2 (Fixed Value Statement)
5	Value Stack at time (1 + 1) = Value Stack at time 2	if 1 + 1 = 2, then Value Stack at time (1 + 1) = Value Stack at time 2 (Substitution)
6	Value Stack at time 2 = [ [ ], [ ] ]	if Value Stack at time (1 + 1) = Value Stack at time 2 and Value Stack at time (1 + 1) = [ [ ], [ ] ], then Value Stack at time 2 = [ [ ], [ ] ] (Transitive Property of Equality Variation 2)

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