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Proof step 19 from proof overwrite-write-page-dirty (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n])
Proof step 21:
files[ino] = mkfile(m4, md0, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m2, m3)), ino ∈ icache, ino ∈ files ⊦ ∀ n. (n ∈ (content ⊕ mkcontent(ino, pcache))[m, buf] ↔ n ∈ content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])) ∧ (content ⊕ mkcontent(ino, pcache))[m, buf][n] = (content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]))[n]

Rule argument

spec: store, inst: file-content name: Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n]) subst: [content0, content] → [ content ⊕ mkcontent (ino, pcache[datakey(ino, m), mkpentry(true, buf)]), (content ⊕ mkcontent(ino, pcache))[m, buf]] flags: <all paths>

Additional information

Used terms: content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]), (content ⊕ mkcontent(ino, pcache))[m, buf]