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Proof step 10 from proof update-keyin-01 (previous step)

∀ r, sk, r0, st. r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis0 ⊦ r -- sk ∈ (update(r0, fis0, st)[r0 -- sk0, val]) ↔ r -- sk ∈ st ∨ r = r0 ∧ (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 9:
∀ r, sk, r0, st. r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis0 ⊦ r -- sk = r0 -- sk0 ∨ r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ (sk = sk0 ∨ sk ∈ fis0)

Rule argument

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

Additional information

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