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Proof step 777 from proof overwrite-write-page-clean (previous step)

files[ino0] = mkfile(m4, md1, m5, content1), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), datakey(ino, n) ∈ pcache, n ∈ content0, ino ∈ files, ino0 ∈ files, ino ∈ icache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ n ∈ content1 ⊕ mkcontent(ino0, pcache) ↔ n ∈ content1 ∨ datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], datakey(ino0, m) = datakey(ino, m), n = m, ino0 ∈ icache, datakey(ino0, m) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 778:
⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache

Rule argument

spec: store, inst: pcache-wb name: In-insert seq: ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache subst: [pe, key0, pcache, key] → [mkpentry(false, buf), datakey(ino, m), pcache, datakey(ino0, n)] flags: <all paths>

Additional information

Used simplifier rules: in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;%in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used terms: mkpentry(false, buf), datakey(ino, m), pcache, datakey(ino0, n)