[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 13 from proof in-put-rkvs (previous step)

∀ rk, st. rk ∈ st[rkvs0] ↔ rk ∈ st ∨ rk ∈ rkvs0 ⊦ rk ∈ (st[rk0, val][rkvs0]) ↔ rk ∈ st ∨ rk = rk0 ∨ rk ∈ rkvs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ rk ∈ rkvs → (st[rk, val][rkvs]) = (st[rkvs][rk, val])
Proof step 7:
¬ ¬ rk0 ∈ rkvs0, ∀ rk, st. rk ∈ st[rkvs0] ↔ rk ∈ st ∨ rk ∈ rkvs0 ⊦ rk ∈ (st[rk0, val][rkvs0]) ↔ rk ∈ st ∨ rk = rk0 ∨ rk ∈ rkvs0
Proof step 12:
¬ rk0 ∈ rkvs0, ∀ rk, st. rk ∈ st[rkvs0] ↔ rk ∈ st ∨ rk ∈ rkvs0 ⊦ rk ∈ (st[rkvs0][rk0, val]) ↔ rk ∈ st ∨ rk = rk0 ∨ rk ∈ rkvs0

Rule argument

[crewrite-arg: put-rkvs-switch , F , [rkvs, val, rk, st] → [rkvs0, val, rk0, st] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (rkvs0, val, rk0, st)]]