Proof: Do Stack At Unchanged 45

Let's prove the following theorem:

if the following are true:
  • expression state at time 45 = "begin_expr"
  • stack at time 45 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

then stack at time 46 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

Proof:

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Given
1 expression state at time 45 = "begin_expr"
2 stack at time 45 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
Proof Table
# Claim Reason
1 stack at time (45 + 1) = stack at time 45 if expression state at time 45 = "begin_expr", then stack at time (45 + 1) = stack at time 45
2 stack at time (45 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] if stack at time (45 + 1) = stack at time 45 and stack at time 45 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time (45 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
3 45 + 1 = 46 45 + 1 = 46
4 stack at time (45 + 1) = stack at time 46 if 45 + 1 = 46, then stack at time (45 + 1) = stack at time 46
5 stack at time 46 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] if stack at time (45 + 1) = stack at time 46 and stack at time (45 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time 46 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

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