Proof: Get Begin Expr Parent 60

Let's prove the following theorem:

if the following are true:

expression state at time 60 = "begin_expr"
the expression at time 60 = __mul__(self.age, 12)
parent stack at time 60 = [ ]

then parent stack at time 61 = [ __mul__(self.age, 12), [ ] ]

Proof:

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Given

1	expression state at time 60 = "begin_expr"
2	the expression at time 60 = `__mul__(self.age, 12)`
3	parent stack at time 60 = [ ]

Proof Table

#	Claim	Reason
1	parent stack at time (60 + 1) = [ `__mul__(self.age, 12)`, parent stack at time 60 ]	if expression state at time 60 = "begin_expr" and the expression at time 60 = `__mul__(self.age, 12)`, then parent stack at time (60 + 1) = [ `__mul__(self.age, 12)`, parent stack at time 60 ] (Begin Expression Parent Rule)
2	[ `__mul__(self.age, 12)`, parent stack at time 60 ] = [ `__mul__(self.age, 12)`, [ ] ]	if parent stack at time 60 = [ ], then [ `__mul__(self.age, 12)`, parent stack at time 60 ] = [ `__mul__(self.age, 12)`, [ ] ] (Substitution)
3	parent stack at time (60 + 1) = [ `__mul__(self.age, 12)`, [ ] ]	if parent stack at time (60 + 1) = [ `__mul__(self.age, 12)`, parent stack at time 60 ] and [ `__mul__(self.age, 12)`, parent stack at time 60 ] = [ `__mul__(self.age, 12)`, [ ] ], then parent stack at time (60 + 1) = [ `__mul__(self.age, 12)`, [ ] ] (Transitive Property of Equality)
4	60 + 1 = 61	60 + 1 = 61 (Fixed Value Statement)
5	parent stack at time (60 + 1) = parent stack at time 61	if 60 + 1 = 61, then parent stack at time (60 + 1) = parent stack at time 61 (Substitution)
6	parent stack at time 61 = [ `__mul__(self.age, 12)`, [ ] ]	if parent stack at time (60 + 1) = parent stack at time 61 and parent stack at time (60 + 1) = [ `__mul__(self.age, 12)`, [ ] ], then parent stack at time 61 = [ `__mul__(self.age, 12)`, [ ] ] (Transitive Property of Equality Variation 2)

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