Proof: Do Control Map At Unchanged 39

Let's prove the following theorem:

if the following are true:

expression state at time 39 = "return"
Control Map at time 39 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 40 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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

Given

1	expression state at time 39 = "return"
2	Control Map at time 39 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof Table

#	Claim	Reason
1	Control Map at time (39 + 1) = Control Map at time 39	if expression state at time 39 = "return", then Control Map at time (39 + 1) = Control Map at time 39 (Return (10))
2	Control Map at time (39 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (39 + 1) = Control Map at time 39 and Control Map at time 39 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (39 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality)
3	39 + 1 = 40	39 + 1 = 40 (Fixed Value Statement)
4	Control Map at time (39 + 1) = Control Map at time 40	if 39 + 1 = 40, then Control Map at time (39 + 1) = Control Map at time 40 (Substitution)
5	Control Map at time 40 = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (39 + 1) = Control Map at time 40 and Control Map at time (39 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 40 = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality Variation 2)

Comments

Please log in to add comments