Proof: Get Begin Expr Parent 13

Let's prove the following theorem:

if the following are true:

expression state at time 13 = "begin_expr"
the expression at time 13 = __eq__(7, 9)
parent stack at time 13 = [ ]

then parent stack at time 14 = [ __eq__(7, 9), [ ] ]

Proof:

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Given

1	expression state at time 13 = "begin_expr"
2	the expression at time 13 = `__eq__(7, 9)`
3	parent stack at time 13 = [ ]

Proof Table

#	Claim	Reason
1	parent stack at time (13 + 1) = [ `__eq__(7, 9)`, parent stack at time 13 ]	if expression state at time 13 = "begin_expr" and the expression at time 13 = `__eq__(7, 9)`, then parent stack at time (13 + 1) = [ `__eq__(7, 9)`, parent stack at time 13 ] (Begin Expression Parent Rule)
2	[ `__eq__(7, 9)`, parent stack at time 13 ] = [ `__eq__(7, 9)`, [ ] ]	if parent stack at time 13 = [ ], then [ `__eq__(7, 9)`, parent stack at time 13 ] = [ `__eq__(7, 9)`, [ ] ] (Substitution)
3	parent stack at time (13 + 1) = [ `__eq__(7, 9)`, [ ] ]	if parent stack at time (13 + 1) = [ `__eq__(7, 9)`, parent stack at time 13 ] and [ `__eq__(7, 9)`, parent stack at time 13 ] = [ `__eq__(7, 9)`, [ ] ], then parent stack at time (13 + 1) = [ `__eq__(7, 9)`, [ ] ] (Transitive Property of Equality)
4	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
5	parent stack at time (13 + 1) = parent stack at time 14	if 13 + 1 = 14, then parent stack at time (13 + 1) = parent stack at time 14 (Substitution)
6	parent stack at time 14 = [ `__eq__(7, 9)`, [ ] ]	if parent stack at time (13 + 1) = parent stack at time 14 and parent stack at time (13 + 1) = [ `__eq__(7, 9)`, [ ] ], then parent stack at time 14 = [ `__eq__(7, 9)`, [ ] ] (Transitive Property of Equality Variation 2)

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