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Proof step 7 from proof update-put-notin (previous step)

∀ r0, st, sk, val. (update(r0, fis0, st)[r0 -- sk, val]) = update(r0, fis0, st[r0 -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r0, fis0, st)[r0 -- sk0, val0][r0 -- sk, val]) = (update(r0, fis0, st[r0 -- sk, val])[r0 -- sk0, val0]), sk = sk0, sk ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 6:
r0 -- sk ≠ r0 -- sk0, ∀ r0, st, sk, val. (update(r0, fis0, st)[r0 -- sk, val]) = update(r0, fis0, st[r0 -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r0, fis0, st)[r0 -- sk, val][r0 -- sk0, val0]) = (update(r0, fis0, st[r0 -- sk, val])[r0 -- sk0, val0]), sk = sk0, sk ∈ fis0

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, r0 -- sk, val0, r0 -- sk0, update(r0, fis0, st)] ,F ,store ,javastore-ostorea ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (val, r0 -- sk, val0, r0 -- sk0, update(r0, fis0, st))]]