Proof: Do Control Map At Unchanged 43

Let's prove the following theorem:

if the following are true:

expression state at time 43 = "iterate_args"
Control Map at time 43 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 44 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof:

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

Given

1	expression state at time 43 = "iterate_args"
2	Control Map at time 43 = [ entry 0: (pair ("while", 2)), [ ] ]

Proof Table

#	Claim	Reason
1	Control Map at time (43 + 1) = Control Map at time 43	if expression state at time 43 = "iterate_args", then Control Map at time (43 + 1) = Control Map at time 43 (Iterate Insn (7))
2	Control Map at time (43 + 1) = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (43 + 1) = Control Map at time 43 and Control Map at time 43 = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time (43 + 1) = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality)
3	43 + 1 = 44	43 + 1 = 44 (Fixed Value Statement)
4	Control Map at time (43 + 1) = Control Map at time 44	if 43 + 1 = 44, then Control Map at time (43 + 1) = Control Map at time 44 (Substitution)
5	Control Map at time 44 = [ entry 0: (pair ("while", 2)), [ ] ]	if Control Map at time (43 + 1) = Control Map at time 44 and Control Map at time (43 + 1) = [ entry 0: (pair ("while", 2)), [ ] ], then Control Map at time 44 = [ entry 0: (pair ("while", 2)), [ ] ] (Transitive Property of Equality Variation 2)

Comments

Please log in to add comments