Proof: Do Stack At Unchanged 78

Let's prove the following theorem:

if the following are true:
  • expression state at time 78 = "call_function_begin"
  • stack at time 78 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

then stack at time 79 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

Proof:

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Given
1 expression state at time 78 = "call_function_begin"
2 stack at time 78 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
Proof Table
# Claim Reason
1 stack at time (78 + 1) = stack at time 78 if expression state at time 78 = "call_function_begin", then stack at time (78 + 1) = stack at time 78
2 stack at time (78 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] if stack at time (78 + 1) = stack at time 78 and stack at time 78 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time (78 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
3 78 + 1 = 79 78 + 1 = 79
4 stack at time (78 + 1) = stack at time 79 if 78 + 1 = 79, then stack at time (78 + 1) = stack at time 79
5 stack at time 79 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] if stack at time (78 + 1) = stack at time 79 and stack at time (78 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time 79 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

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