Proof: Do Stack At Unchanged 50

Let's prove the following theorem:

if the following are true:
  • expression state at time 50 = "return"
  • stack at time 50 = [ 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 51 = [ 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:

View as a tree | View dependent proofs | Try proving it

Given
1 expression state at time 50 = "return"
2 stack at time 50 = [ 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 (50 + 1) = stack at time 50 if expression state at time 50 = "return", then stack at time (50 + 1) = stack at time 50
2 stack at time (50 + 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 (50 + 1) = stack at time 50 and stack at time 50 = [ 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 (50 + 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 50 + 1 = 51 50 + 1 = 51
4 stack at time (50 + 1) = stack at time 51 if 50 + 1 = 51, then stack at time (50 + 1) = stack at time 51
5 stack at time 51 = [ 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 (50 + 1) = stack at time 51 and stack at time (50 + 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 51 = [ 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")), [ ] ], [ ] ]

Comments

Please log in to add comments