Proof: Do Control Map At Unchanged 54

Let's prove the following theorem:

if the following are true:

expression state at time 54 = "return"
Control Map at time 54 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 55 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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

Given

1	expression state at time 54 = "return"
2	Control Map at time 54 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof Table

#	Claim	Reason
1	Control Map at time (54 + 1) = Control Map at time 54	if expression state at time 54 = "return", then Control Map at time (54 + 1) = Control Map at time 54 (Return (10))
2	Control Map at time (54 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (54 + 1) = Control Map at time 54 and Control Map at time 54 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (54 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality)
3	54 + 1 = 55	54 + 1 = 55 (Fixed Value Statement)
4	Control Map at time (54 + 1) = Control Map at time 55	if 54 + 1 = 55, then Control Map at time (54 + 1) = Control Map at time 55 (Substitution)
5	Control Map at time 55 = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (54 + 1) = Control Map at time 55 and Control Map at time (54 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 55 = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality Variation 2)

Comments

Please log in to add comments