Proof: Do Stack At Unchanged 68

Let's prove the following theorem:

if the following are true:
  • expression state at time 68 = "return"
  • stack at time 68 = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]

then stack at time 69 = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]

Proof:

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Given
1 expression state at time 68 = "return"
2 stack at time 68 = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]
Proof Table
# Claim Reason
1 stack at time (68 + 1) = stack at time 68 if expression state at time 68 = "return", then stack at time (68 + 1) = stack at time 68
2 stack at time (68 + 1) = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ] if stack at time (68 + 1) = stack at time 68 and stack at time 68 = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ], then stack at time (68 + 1) = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]
3 68 + 1 = 69 68 + 1 = 69
4 stack at time (68 + 1) = stack at time 69 if 68 + 1 = 69, then stack at time (68 + 1) = stack at time 69
5 stack at time 69 = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ] if stack at time (68 + 1) = stack at time 69 and stack at time (68 + 1) = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ], then stack at time 69 = [ program context with variables: [ entry p: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 9 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]

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