Proof: Do Stack At Unchanged 35

Let's prove the following theorem:

if the following are true:
  • expression state at time 35 = "begin_expr"
  • stack at time 35 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]

then stack at time 36 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]

Proof:

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

Given
1 expression state at time 35 = "begin_expr"
2 stack at time 35 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]
Proof Table
# Claim Reason
1 stack at time (35 + 1) = stack at time 35 if expression state at time 35 = "begin_expr", then stack at time (35 + 1) = stack at time 35
2 stack at time (35 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ] if stack at time (35 + 1) = stack at time 35 and stack at time 35 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ], then stack at time (35 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]
3 35 + 1 = 36 35 + 1 = 36
4 stack at time (35 + 1) = stack at time 36 if 35 + 1 = 36, then stack at time (35 + 1) = stack at time 36
5 stack at time 36 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ] if stack at time (35 + 1) = stack at time 36 and stack at time (35 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ], then stack at time 36 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 8 tab: 0) and control map: [ entry 0: (pair ("class", "Person")), [ ] ], [ ] ]

Comments

Please log in to add comments