Proof: Do Stack At Unchanged 19

Let's prove the following theorem:

if the following are true:
  • expression state at time 19 = "iterate_args"
  • stack at time 19 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

then stack at time 20 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

Proof:

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Given
1 expression state at time 19 = "iterate_args"
2 stack at time 19 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
Proof Table
# Claim Reason
1 stack at time (19 + 1) = stack at time 19 if expression state at time 19 = "iterate_args", then stack at time (19 + 1) = stack at time 19
2 stack at time (19 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] if stack at time (19 + 1) = stack at time 19 and stack at time 19 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time (19 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
3 19 + 1 = 20 19 + 1 = 20
4 stack at time (19 + 1) = stack at time 20 if 19 + 1 = 20, then stack at time (19 + 1) = stack at time 20
5 stack at time 20 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] if stack at time (19 + 1) = stack at time 20 and stack at time (19 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time 20 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]

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