Proof: Get Begin Expr Parent 18

Let's prove the following theorem:

if the following are true:

expression state at time 18 = "begin_expr"
the expression at time 18 = self."x" = 0
parent stack at time 18 = [ ]

then parent stack at time 19 = [ self."x" = 0, [ ] ]

Proof:

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Given

1	expression state at time 18 = "begin_expr"
2	the expression at time 18 = self."x" = 0
3	parent stack at time 18 = [ ]

Proof Table

#	Claim	Reason
1	parent stack at time (18 + 1) = [ self."x" = 0, parent stack at time 18 ]	if expression state at time 18 = "begin_expr" and the expression at time 18 = self."x" = 0, then parent stack at time (18 + 1) = [ self."x" = 0, parent stack at time 18 ] (Set Attribute Begin Parent Property)
2	[ self."x" = 0, parent stack at time 18 ] = [ self."x" = 0, [ ] ]	if parent stack at time 18 = [ ], then [ self."x" = 0, parent stack at time 18 ] = [ self."x" = 0, [ ] ] (Substitution)
3	parent stack at time (18 + 1) = [ self."x" = 0, [ ] ]	if parent stack at time (18 + 1) = [ self."x" = 0, parent stack at time 18 ] and [ self."x" = 0, parent stack at time 18 ] = [ self."x" = 0, [ ] ], then parent stack at time (18 + 1) = [ self."x" = 0, [ ] ] (Transitive Property of Equality)
4	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
5	parent stack at time (18 + 1) = parent stack at time 19	if 18 + 1 = 19, then parent stack at time (18 + 1) = parent stack at time 19 (Substitution)
6	parent stack at time 19 = [ self."x" = 0, [ ] ]	if parent stack at time (18 + 1) = parent stack at time 19 and parent stack at time (18 + 1) = [ self."x" = 0, [ ] ], then parent stack at time 19 = [ self."x" = 0, [ ] ] (Transitive Property of Equality Variation 2)

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