Proof: Get Begin Expr State 19

Let's prove the following theorem:

if the following are true:

the expression at time 19 = "Mexico"
expression state at time 19 = "begin_expr"
"Mexico" is constant
parent stack at time 19 = [ entry "MX": "Mexico", [ {"ES": "Estonia", "MX": "Mexico"}, [ ] ] ]

then expression state at time 20 = "return"

Proof:

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Given

1	the expression at time 19 = "Mexico"
2	expression state at time 19 = "begin_expr"
3	"Mexico" is constant
4	parent stack at time 19 = [ entry "MX": "Mexico", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ]

Proof Table

#	Claim	Reason
1	expression state at time (19 + 1) = "return"	if expression state at time 19 = "begin_expr" and the expression at time 19 = "Mexico" and "Mexico" is constant and parent stack at time 19 = [ entry "MX": "Mexico", [ `{"ES": "Estonia", "MX": "Mexico"}`, [ ] ] ], then expression state at time (19 + 1) = "return" (Evaluate Constant Argument State Property)
2	19 + 1 = 20	19 + 1 = 20 (Fixed Value Statement)
3	expression state at time (19 + 1) = expression state at time 20	if 19 + 1 = 20, then expression state at time (19 + 1) = expression state at time 20 (Substitution)
4	expression state at time 20 = "return"	if expression state at time (19 + 1) = expression state at time 20 and expression state at time (19 + 1) = "return", then expression state at time 20 = "return" (Transitive Property of Equality Variation 2)

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