Proof: Get Begin Expr Parent 67

Let's prove the following theorem:

if the following are true:

expression state at time 67 = "begin_expr"
the expression at time 67 = joe.jump()
parent stack at time 67 = [ ]

then parent stack at time 68 = [ joe.jump(), [ ] ]

Proof:

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Given

1	expression state at time 67 = "begin_expr"
2	the expression at time 67 = `joe.jump()`
3	parent stack at time 67 = [ ]

Proof Table

#	Claim	Reason
1	parent stack at time (67 + 1) = [ `joe.jump()`, parent stack at time 67 ]	if expression state at time 67 = "begin_expr" and the expression at time 67 = `joe.jump()`, then parent stack at time (67 + 1) = [ `joe.jump()`, parent stack at time 67 ] (Begin Method Arguments (2))
2	[ `joe.jump()`, parent stack at time 67 ] = [ `joe.jump()`, [ ] ]	if parent stack at time 67 = [ ], then [ `joe.jump()`, parent stack at time 67 ] = [ `joe.jump()`, [ ] ] (Substitution)
3	parent stack at time (67 + 1) = [ `joe.jump()`, [ ] ]	if parent stack at time (67 + 1) = [ `joe.jump()`, parent stack at time 67 ] and [ `joe.jump()`, parent stack at time 67 ] = [ `joe.jump()`, [ ] ], then parent stack at time (67 + 1) = [ `joe.jump()`, [ ] ] (Transitive Property of Equality)
4	67 + 1 = 68	67 + 1 = 68 (Fixed Value Statement)
5	parent stack at time (67 + 1) = parent stack at time 68	if 67 + 1 = 68, then parent stack at time (67 + 1) = parent stack at time 68 (Substitution)
6	parent stack at time 68 = [ `joe.jump()`, [ ] ]	if parent stack at time (67 + 1) = parent stack at time 68 and parent stack at time (67 + 1) = [ `joe.jump()`, [ ] ], then parent stack at time 68 = [ `joe.jump()`, [ ] ] (Transitive Property of Equality Variation 2)

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