Proof: Get Begin Expr Params 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)
arguments stack at time 13 = [ ]

then arguments stack at time 14 = [ [ 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	arguments stack at time 13 = [ ]

Proof Table

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

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