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Proof step 6 from proof update-keyin (previous step)

∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ (update(r, fis0, st)[r -- sk0, val]) ↔ r0 -- sk ∈ st, sk = sk0, sk ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st
Proof step 5:
∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk = r -- sk0 ∨ r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st, sk = sk0, sk ∈ fis0

Rule argument

[speclemmaarg: ,rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st ,[val, rk0, st, rk] → [val, r -- sk0, update(r, fis0, st), r0 -- sk] ,F ,store ,javastore-ostorea ,In-insert ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, r -- sk0, update(r, fis0, st), r0 -- sk)]]