Proof: Get Begin Expr Parent 54

Let's prove the following theorem:

if the following are true:
  • expression state at time 54 = "begin_expr"
  • the expression at time 54 = p.age_in_months()
  • parent stack at time 54 = [ ]

then parent stack at time 55 = [ p.age_in_months(), [ ] ]

Proof:

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Given
1 expression state at time 54 = "begin_expr"
2 the expression at time 54 = p.age_in_months()
3 parent stack at time 54 = [ ]
Proof Table
# Claim Reason
1 parent stack at time (54 + 1) = [ p.age_in_months(), parent stack at time 54 ] if expression state at time 54 = "begin_expr" and the expression at time 54 = p.age_in_months(), then parent stack at time (54 + 1) = [ p.age_in_months(), parent stack at time 54 ]
2 [ p.age_in_months(), parent stack at time 54 ] = [ p.age_in_months(), [ ] ] if parent stack at time 54 = [ ], then [ p.age_in_months(), parent stack at time 54 ] = [ p.age_in_months(), [ ] ]
3 parent stack at time (54 + 1) = [ p.age_in_months(), [ ] ] if parent stack at time (54 + 1) = [ p.age_in_months(), parent stack at time 54 ] and [ p.age_in_months(), parent stack at time 54 ] = [ p.age_in_months(), [ ] ], then parent stack at time (54 + 1) = [ p.age_in_months(), [ ] ]
4 54 + 1 = 55 54 + 1 = 55
5 parent stack at time (54 + 1) = parent stack at time 55 if 54 + 1 = 55, then parent stack at time (54 + 1) = parent stack at time 55
6 parent stack at time 55 = [ p.age_in_months(), [ ] ] if parent stack at time (54 + 1) = parent stack at time 55 and parent stack at time (54 + 1) = [ p.age_in_months(), [ ] ], then parent stack at time 55 = [ p.age_in_months(), [ ] ]

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