Proof: Get Begin Expr Params 3

Let's prove the following theorem:

if the following are true:

expression state at time 3 = "begin_expr"
the expression at time 3 = entry "ES": "Estonia"
arguments stack at time 3 = [ [ entry "MX": "Mexico", [ ] ], [ ] ]

then arguments stack at time 4 = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ]

Proof:

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Given

1	expression state at time 3 = "begin_expr"
2	the expression at time 3 = entry "ES": "Estonia"
3	arguments stack at time 3 = [ [ entry "MX": "Mexico", [ ] ], [ ] ]

Proof Table

#	Claim	Reason
1	arguments stack at time (3 + 1) = [ [ "ES", [ "Estonia", [ ] ] ], arguments stack at time 3 ]	if expression state at time 3 = "begin_expr" and the expression at time 3 = entry "ES": "Estonia", then arguments stack at time (3 + 1) = [ [ "ES", [ "Estonia", [ ] ] ], arguments stack at time 3 ] (Entry Arguments Property)
2	[ [ "ES", [ "Estonia", [ ] ] ], arguments stack at time 3 ] = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ]	if arguments stack at time 3 = [ [ entry "MX": "Mexico", [ ] ], [ ] ], then [ [ "ES", [ "Estonia", [ ] ] ], arguments stack at time 3 ] = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ] (Substitution)
3	arguments stack at time (3 + 1) = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ]	if arguments stack at time (3 + 1) = [ [ "ES", [ "Estonia", [ ] ] ], arguments stack at time 3 ] and [ [ "ES", [ "Estonia", [ ] ] ], arguments stack at time 3 ] = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ], then arguments stack at time (3 + 1) = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ] (Transitive Property of Equality)
4	3 + 1 = 4	3 + 1 = 4 (Fixed Value Statement)
5	arguments stack at time (3 + 1) = arguments stack at time 4	if 3 + 1 = 4, then arguments stack at time (3 + 1) = arguments stack at time 4 (Substitution)
6	arguments stack at time 4 = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ]	if arguments stack at time (3 + 1) = arguments stack at time 4 and arguments stack at time (3 + 1) = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ], then arguments stack at time 4 = [ [ "ES", [ "Estonia", [ ] ] ], [ [ entry "MX": "Mexico", [ ] ], [ ] ] ] (Transitive Property of Equality Variation 2)

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