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Proof step 488 from proof overwrite-write-page-clean (previous step)

files[ino0] = mkfile(m6, md1, m7, content), icache[ino0] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ m ∈ content, ino ∈ icache, m ∈ mkcontent(ino0, pcache), (m ∈ content ⊕ mkcontent(ino0, pcache) ↔ m ∈ content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content ⊕ mkcontent(ino0, pcache))[m] = (content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 489:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino0] = mkfile(m6, md1, m7, content), ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ ino ∈ icache, m ∈ content, datakey(ino0, m) ∈ pcache, (datakey(ino0, m) = datakey(ino, m) → m ∈ content ⊕ mkcontent(ino0, pcache)) ∧ (content ⊕ mkcontent(ino0, pcache))[m] = (content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[m]

Rule argument

Additional information

Used simplifier rules: in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;%in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)