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Proof step 37 from proof onlymod-is-update (previous step)

(st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]), rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk)), # st0 = m + 1, validFields(r0, fis, st0 -- (r0 -- sk)), r0 ∈ st0, r0 ∈ st1, onlyModified(r0, st0, st1), r0 -- sk ∈ st0, r0 -- sk ∈ st1, ∀ rk. (rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk))) ∧ (st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]) ⊦ st0 = ∅, st0[r0 -- sk] = st1[r0 -- sk], rk ∈ st1 ↔ rk = r0 -- sk ∨ rk ∈ update(r0, fis, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ rk ≠ rk0 → (st -- rk0)[rk] = st[rk]
Proof step 30:
⊦ r -- sk ∈ update(r0, fis, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis
Proof step 31:
⊦ ¬ sk ∈ fis → (update(r, fis, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 36:
rk ≠ r0 -- sk, st1[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]), rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk)), # st0 = m + 1, validFields(r0, fis, st0 -- (r0 -- sk)), r0 ∈ st0, r0 ∈ st1, onlyModified(r0, st0, st1), r0 -- sk ∈ st0, r0 -- sk ∈ st1, ∀ rk. (rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk))) ∧ (st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]) ⊦ st0 = ∅, st0[r0 -- sk] = st1[r0 -- sk], rk ∈ st1 ↔ rk = r0 -- sk ∨ rk ∈ update(r0, fis, st0)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st -- rk0)[rk] = st[rk] ,[rk, rk0, st] → [rk, r0 -- sk, st1] ,F ,store ,javastore ,Del-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st -- rk)[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ rk ∈ st -- rk0 ↔ rk ≠ rk0 ∧ rk ∈ st])], [EXTRATERMS : (rk, r0 -- sk, st1)]]