Proof: Do Variables At Unchanged 30

Let's prove the following theorem:

if the following are true:
  • expression state at time 30 = "return"
  • Variables Map at time 30 = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ]

then Variables Map at time 31 = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ]

Proof:

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Given
1 expression state at time 30 = "return"
2 Variables Map at time 30 = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ]
Proof Table
# Claim Reason
1 Variables Map at time (30 + 1) = Variables Map at time 30 if expression state at time 30 = "return", then Variables Map at time (30 + 1) = Variables Map at time 30
2 Variables Map at time (30 + 1) = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ] if Variables Map at time (30 + 1) = Variables Map at time 30 and Variables Map at time 30 = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ], then Variables Map at time (30 + 1) = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ]
3 30 + 1 = 31 30 + 1 = 31
4 Variables Map at time (30 + 1) = Variables Map at time 31 if 30 + 1 = 31, then Variables Map at time (30 + 1) = Variables Map at time 31
5 Variables Map at time 31 = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ] if Variables Map at time (30 + 1) = Variables Map at time 31 and Variables Map at time (30 + 1) = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ], then Variables Map at time 31 = [ entry self: (Python reference 0), [ entry first_name: "John", [ entry last_name: "Smith", [ entry age: 25, [ ] ] ] ] ]

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